Zurich Open Repository and Archive University of Zurich Main Library Strickhofstrasse 39 CH-8057 Zurich www.zora.uzh.ch

Year: 2010

Structural studies of h-BN and graphene single-layers on transition-metal surfaces

Martoccia, Domenico

Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-163948 Dissertation Published Version

Originally published at: Martoccia, Domenico. Structural studies of h-BN and graphene single-layers on transition-metal surfaces. 2010, University of Zurich, Faculty of Science. Structural Studies of h-BN and Graphene Single-Layers on Transition-Metal Surfaces

Dissertation zur Erlangung der naturwissenschaftlichen Doktorw¨urde (Dr. sc. nat.) vorgelegt der Mathematisch-naturwissenschaftlichen Fakult¨at der Universit¨at Z¨urich von

Domenico Martoccia aus Italien

Promotionskomitee Prof. Dr. Bruce D. Patterson (Vorsitz) Prof. Dr. Hugo Keller (Leitung der Dissertation) Prof. Dr. Philip R. Willmott Prof. Dr. Thomas Greber Prof. Dr. Herbert Over

Z¨urich, 2010

iii

The whole of science is nothing more than a refinement of everyday thinking

Albert Einstein (1879 – 1955)

To my family ii

This work is copyrighted by Domenico Martoccia and the Surface Diffraction Group of the Materials Science Beamline at the Swiss Light Source, Paul Scherrer Institut, Switzerland, unless stated otherwise in the text. Reprints and any use of text, tables or figures need the permission of the author or the group.

A This document was prepared using LTEX2ε using Philip R. Willmott’s customized version of the document class file book.cls, named coolhab.cls, and a customized bibliography style created using the custom-bib package.

c Domenico Martoccia, Villigen, 2010

Printed in Switzerland Acknowledgements

Early on in this project, it became clear to me that a researcher cannot complete a Ph.D. in physics alone. Especially when working at a synchrotron, the collaboration with other groups and people is one of the key features for success. Although the list of individuals I wish to thank extends beyond the limits of this format, I would like to thank the following persons for their dedication, and support throughout my entire project. First I thank Bruce Patterson, for having given me the opportunity to perform this Ph.D. in an institute, as excellent as PSI. A small part of his motivation for science and some of his great ideas are crystallized in this work, and formed the start of this project. I want to thank him not only for the constant scientific input during my work, but also for the way he explained to me complicated physical relationships in the simplest way. My biggest thanks go to Philip Willmott, he has made this work a pleasure. He guided me in his friendly way through this work and always found time for answering my questions, which often led to interesting discussions. Also, he was always there, not only when we were on the way of publishing, but also when my motivation was passing through minima – he always found the right words for getting me out again. He assisted in all of my beamtimes and made even the longest night shifts interesting and humorous. I really want to thank him also for his friendship; beside being an excellent scientist he is a person of good nature. I want to thank Thomas Greber and Thomas Brugger for their scientific input on the subject of nanomeshes. This work was only possible with their ideas of experiments, the way they pushed the collaboration between the Universit¨atZ¨urich and PSI, as well as the great sample quality they provided and the carefully prepared beamtimes, I thank them also for their friendliness. My thanks go also to Herbert Over and Hugo Keller. As part of the Promotionskomitee,

–iii– iv

they supported me whenever their help was needed. My deeply-felt thanks go also to Matts Bj¨orck and my co-students in the Surface Diffraction group, Roger Herger, Christian Schlep¨utz and Stephan Pauli. Many of the results presented in this work rely on the great expertize in python and Matts’ program GenX, which he adapted specifically for this work. All of them I thank for their involvement during the beamtimes, for the lively and interesting discussions, and for their friendships. I thank Oliver Bunk for his great help in simulations with fit and for having provided the basis for the understanding of diffraction patterns of nanomeshes. His calm and straightforward thinking skills impressed me. Without the enormous assistance of all the technicians involved in this work, none of the science would have been possible. I would like to thank our in-house engineer Dominik Meister and technician Michael Lange for helping me in improving the experimental setup needed for this work. With their careful work and their technical skills they made the accurate mea- surements possible. I also thank Rolf Schelldorfer for the help in designing and constructing a transportable UHV-baby chamber, which was essential for the combination of complemen- tary techniques, and Martin K¨ockner for his help in adapting it and make it suitable for the ESCA-lab at the Universi¨atZ¨urich. I want to thank also Fabia Gozzo, Antonio Cervellino, Amela Groso and Marco Stampanoni, as present and past members of the Materials Science Beamline group. They always made the atmosphere within the group very pleasant. For good data analysis, good data is needed, which was guaranteed here by combining synchrotron light with an excellent detector. I thank all the SLS machine people for providing a constant and high beam quality for all of my experiments, but the in-house detector group and DECTRIS for having provided the surface x-ray diffraction station with a detector as outstanding as the PILATUS 100k. My very special thanks go to Catherine, the french woman I met on the train years ago. I thank her for the patience, for the encouraging words, and for her positive way of thinking, she has helped me to remain steadfast and to never bend to difficulty. There are no words for saying how grateful I am to her love, which she expresses for me every day. Nothing of all this would have ever happened without my mother and my brother Michele. Without their encouraging words and love, without their patience and support, I would have v

never been able to pursue these studies. Although my Dad cannot physically share this moment with me anymore, I am sure that he is proud of what his endless love for me has led to. Thank you, Dad.

Abstract

Nanotemplates have attracted considerable attention in recent years. They can be used to produce well-ordered surface arrays of single molecules and nanoparticles with nanometer-scale periodicity. In particular, self-organized nanotemplates are increasingly becoming the focus of investigations, due to their ease of fabrication. When hexagonal boron nitride (h-BN)- and graphene single-layers are grown on substrates with slightly different lattice parameters, such as Rh(111) or Ru(0001), they form commensurate superstructures. Due to the lattice mismatch and the resulting periodically varying strength of interaction with the substrate across the surface, the monolayers tend to corrugate, that is, their separation from the substrate varies across the surface in a regular way. The electronic properties of these sp2-hybridized layers can be modified, depending on the substrates they are grown on and their lattice mismatch to them. In particular, graphene, which as a freestanding layer is a gapless semiconductor with a remarkably high electron mobility and a small spin-orbit-interaction, and hence an ideal material for spintronics and other technical applications, can have an energy band gap when grown on a substrate and become a semiconductor, which for technological applications is of high interest. This complex behaviour of the electronic properties is strongly correlated to the changes in the atomic structure of both the film and substrate. An exact knowledge of the atomic structure of these systems is essential to understand their electronic and physical properties. The availability of intense 3rd generation synchrotron sources has allowed experiments on elastic scattering and diffraction by surfaces to be realistic, despite the fact that the interaction of photons with matter is weak. Surface x-ray diffraction (SXRD) offers nowadays unique possibilities to study the structure of thin films and interfaces with picometer resolution. When dealing with x-ray diffraction data, one is confronted with the phase problem – the

–vii– viii

phase is lost, due to the fact that one does not measure the complex structure factors (which have an amplitude and phase), but the intensities, which are the absolute squares of the structure factors. To overcome this problem SXRD relies on traditional model refinement. Model refinement requires a starting model which is sufficiently close to the real structure and an appropriate parametrization of the system. Therefore complementary methods are of enormous importance. They are not only a big help for the parametrization, but also give additional physical information, which can be essential for successfully finding the solution of a surface structure. This thesis describes structural studies using SXRD of the sp2-hybridized layers h-BN and graphene, grown on rhodium and ruthenium. Analysis of such superstructures using SXRD is only possible by a parametrization scheme developed as part of this thesis, in conjunction with complementary methods such as scanning tunneling microscopy (STM), low-energy electron- diffraction (LEED) and ultraviolet photoelectron spectroscopy (UPS). Systematic structural studies on h-BN/Rh(111), h-BN/Ru(0001) and graphene/Ru(0001) are presented: In h-BN/Rh(111) the structure is shown to be a commensurate corrugated 13-on-12 su- perstructure. Its commensurability up to high temperatures proves a strong bonding to the substrate. Furthermore, the topmost surface region of the substrate does not thermally expand when the temperature is raised from room temperature to about 200oC, another manifestation of strong bonding to the surface. The h-BN/Ru(0001) system exhibits a commensurate 14-on-13 superstructure. This result was surprising as simple arguments based on the known thermal expansion coefficients of bulk h- BN and Ru would lead to expect a 13-on-12 structure. However, the particularly strong bonding of h-BN to Ru results in an increase in the tightly bound hole region of the superstructure, allowing it to assume a longer size than at first expected. In the case of graphene/Ru(0001), a surprisingly large superstructure was found, (25 × 25) carbon atoms matching on (23×23) ruthenium atoms. Strong oscillations on the superstructure rods prove a corrugation of the substrate down to several monolayers. Using genetic algorithms, crystal truncation and superstructure rod intensities have been fitted after a parametrization of the problem with less than 30 parameters. A chiral surface, caused by the breaking of the surface symmetry has been observed, induced by the associated much lower elastic energy. Zusammenfassung

In den letzten Jahren haben Nanotemplates grosse Beachtung gefunden. Sie k¨onnen zur Pro- duktion einzelner, regelm¨assig angeordneten Molek¨ulen und Nanopartikeln auf Oberfl¨achen mit Nanometer-Skala Periodizit¨at, verwendet werden. Vor allem selbstorganisierte Nanotemplates sind aufgrund ihrer einfachen Herstellung zunehmend in den Fokus der Untersuchungen ger¨uckt. Wenn einzelne hexagonale Bornitrid (h-BN)- und Graphen-Schichten auf Ubergangsmetallen¨ mit leicht unterschiedlichen Gitterkonstanten, wie Rh(111) oder Ru(0001) gewachsen werden, bilden sie kommensurable Uberstrukturen.¨ Aufgrund der Gitterfehlanpassung und der da- raus resultierenden, sich regelm¨assig ¨andernden St¨arke der Wechselwirkung mit dem Substrat entlang der Oberfl¨ache, neigen die Monolagen dazu, zu korrugieren, das heisst, ihr Abstand zum Substrat variiert in einer periodischen Art und Weise. Die elektronischen Eigenschaften dieser sp2-hybridisierten Schichten k¨onnen, abh¨angig vom Substrat auf dem sie gewachsen sind und deren Gitterfehlanpassungen modifiziert werden. Insbesondere Graphen, das als freiste- hende Schicht ein Halbleiter ohne Bandl¨ucke ist, zeigt eine bemerkenswert hohe Mobilit¨atder Elektronen und eine kleine Spin-Bahn-Kopplung. Es ist daher ein ideales Material f¨ur Spin- tronik und andere technische Anwendungen. Wenn es auf einem Substrat gewachsen ist, kann es eine Energie-Bandl¨ucke aufweisen, und ein richtiger Halbleiter werden, was f¨ur elektronis- che Applikationen von grossem Interesse ist. Dieses komplexe Verhalten der elektronischen Eigenschaften korreliert stark mit den Anderungen¨ in der atomaren Struktur der adsorbierten Monolage wie auch des Substrates. Deshalb ist eine genaue Kenntnis der atomaren Struk- tur dieser Systeme f¨ur das Verst¨andnis ihrer elektronischen und physikalischen Eigenschaften entscheidend. Die Verf¨ugbarkeit von Synchrotronquellen der 3. Generation erm¨oglicht Versuche mit elastis- cher Streuung und Beugung an Oberfl¨achen, obwohl die Wechselwirkung von Photonen mit Ma-

–ix– x

terie schwach ist. Oberfl¨achenr¨ontgenbeugung (SXRD) bietet heute einzigartige M¨oglichkeiten zur Untersuchung der Struktur von d¨unnen Schichten und Grenzfl¨achen mit hoher r¨aumlicher Aufl¨osung. Bei der Aufnahme von R¨ontgenbeugungsdaten ist man mit dem Phasenproblem konfrontiert – die Phase geht verloren, weil man nicht die komplexen Strukturfaktoren (die eine Amplitude und eine Phase besitzen), sondern aber die Intensit¨aten misst, sprich die Betragsquadrate der Strukturfaktoren. Um dieses Problem zu umgehen, setzt die Oberfl¨achenr¨ontgen- beu- gung auf die traditionelle Strukturverfeinerung der Modelle. Dies erfordert eine geeignete Parametrisierung des Systems und ein Startmodell, das nahe genug an der wahren Struktur ist. Daher sind komplement¨are Methoden von enormer Bedeutung. Sie sind nicht nur eine grosse Hilfe bei der Modellierung, sondern geben auch zus¨atzliche physikalische Informationen, die f¨ur das erfolgreiche L¨osen einer Oberfl¨achenstruktur von wesentlicher Bedeutung sind. Diese Arbeit beschreibt eine strukturelle Untersuchung der sp2-hybridisierten Schichten h- BN und Graphen, gewachsen auf Rhodium und Ruthenium. Die Analyse solcher Strukturen mit SXRD ist nur dank einer Parametrisierung m¨oglich, die in dieser Arbeit beschrieben ist, in Verbindung mit komplement¨aren Methoden, wie der Rastertunnelmikroskopie (STM), der niederenergetischen Elektronenbeugung (LEED) und der Ultraviolett-Photoelektronenspektroskopie (UPS). Strukturanalysen der Systeme h-BN/Rh(111), h-BN/Ru(0001) und Graphen/Ru(0001) wer- den vorgestellt: In h-BN/Rh(111) ist die gefundene Uberstruktur¨ eine 13-auf-12. Die Kom- mensurabilit¨atbis zu hohen Temperaturen deutet auf eine starke Bindung an das Substrat hin. Dazu kommt, dass sich die oberste Schicht des Substrates thermisch nicht ausdehnt, wenn die Temperatur von Raumtemperatur auf ca. 200oC erh¨oht wird, ein weiteres Zeichen der starken Bindung zwischen der Monolage und dem Substrat. Die h-BN/Ru(0001) Struktur weist eine wohlgeordnete 14-auf-13 Uberstruktur¨ auf. Dieses Ergebnis kam ¨uberraschend, da einfache Argumente, die auf den bekannten thermischen Aus- dehnungskoeffizienten der Volumenfestk¨orper h-BN und Ruthenium basieren, zu einer 13-auf-12 Struktur f¨uhren w¨urden. Die besonders starke Bindung von h-BN zu Ruthenium aber f¨uhrt zu einer Vergr¨osserung der fest gebundenen Lochbereiche in der Uberstruktur,¨ so dass es zu einer gr¨osseren Struktur f¨uhrt, als zun¨achst erwartet. Im Falle von Graphen/Ru(0001), wurde eine ¨uberraschend grosse Uberstruktur¨ gefunden, xi

(25 × 25) Kohlenstoffatome passen auf (23 × 23) Rutheniumatome. Starke Oszillationen in den Uberstrukturgitterst¨aben¨ beweisen, dass das Substrat bis zu mehreren Monolagen tief korrugiert ist. Mit Hilfe eines auf genetischen Algorithmen basierenden Programmpakets wurde ein Modell mit weniger als 30 Parametern verfeinert, um die Intensit¨aten von Grundgitter- und Uberstrukturgitterst¨aben¨ m¨oglichst gut wiederzugeben. Eine chirale Oberfl¨ache, hervorgerufen durch einen Symmetriebruch wurde beobachtet. Letzterer wurde durch die damit verbundene viel niedrigere elastische Energie induziert.

Contents

Acknowledgments iii

Abstract vii

Zusammenfassung ix

Contents xiii

List of Figures xvii

1 Introduction 1

2 Surface x-ray diffraction (SXRD) 7 2.1 Introduction ...... 7 2.2 Theory ...... 9 2.2.1 Bulk diffraction ...... 9 2.2.1.1 Bragg’s Law ...... 9 2.2.1.2 Lattice and reciprocal lattice ...... 10 2.2.1.3 The Laue condition ...... 11 2.2.1.4 The Ewald sphere construction ...... 12 2.2.1.5 The convolution theorem ...... 13 2.2.1.6 Diffraction from an ideal infinite crystal ...... 14 2.2.1.7 Structure factors ...... 16 2.2.1.8 Scattering from a crystal ...... 16 2.2.1.9 The lattice sum ...... 17

–xiii– xiv CONTENTS

2.2.1.10 Argand diagram ...... 17 2.2.1.11 Intensity and the phase problem ...... 18 2.2.2 Diffraction from a surface ...... 19 2.2.2.1 Crystal truncation rods ...... 19 2.2.2.2 Structure factor of a surface ...... 19 2.2.2.3 Intensity ...... 21 2.2.2.4 Debye-Waller factor and occupation ...... 21 2.2.2.5 Superstructure rods ...... 22 2.3 Experimental Setup ...... 22 2.3.1 The Materials Science beamline ...... 22 2.3.2 The diffractometer ...... 23 2.3.3 UHV-baby chamber ...... 24 2.3.4 The PILATUS 100k detector ...... 26 2.4 Data recording, extraction and correction ...... 27 2.4.1 Rocking scan ...... 29 2.4.2 Stationary mode ...... 29 2.4.2.1 Limitations of the stationary mode ...... 29 2.4.3 h- or k- scan ...... 30 2.4.4 Extraction and correction ...... 30 2.5 Fitting using Genetic Algorithms ...... 31 Bibliography ...... 33

3 Complementary methods 37 3.1 Introduction ...... 37 3.2 Scanning tunneling microscopy (STM) ...... 37 3.3 Low-energy electron-diffraction (LEED) ...... 39 3.4 Ultraviolet Photoelectron Spectroscopy (UPS) ...... 40 Bibliography ...... 41

4 Nanomeshes 43 4.1 Introduction ...... 43 4.2 hcp(0001)- and fcc(111)-surfaces ...... 44 CONTENTS xv

4.3 sp2-hybridization ...... 46 4.4 Moir´epatterns ...... 46 4.5 Hexagonal Boron Nitride (h-BN) on transition metal surfaces ...... 47 4.6 Graphene on transition metal surfaces ...... 50 4.6.1 The Mermin-Wagner Theorem ...... 54 4.7 Nanomeshes investigated with LEED and SXRD ...... 54 Bibliography ...... 57

5 Surface X-ray diffraction study of boron-nitride nanomesh in air 63

6 h-BN on Rh(111): Persistence of a 13-on-12 superstructure 69

7 h-BN on Ru(0001) nanomesh: A 14-on-13 superstructure 75

8 Graphene on Ru(0001): A 25×25 Supercell 81

9 Graphene on Ru(0001): A corrugated and chiral structure 87

10 Conclusions 101

Curriculum vitae 103

Publication List 105

List of Figures

2.1 (a) Braggs Law (b) Zoom region of Braggs Law ...... 10 2.2 The Laue conditions ...... 11 2.3 The Ewald Sphere ...... 13 2.4 (a) Convolution theorem: The crystal (b) Convolution theorem: The diffraction pattern of a crystal ...... 15 2.5 The Argand diagram ...... 18 2.6 (a) Convolution theorem: The crystal surface (b) Convolution theorem: The crystal truncation rods ...... 20 2.7 The MS-beamline ...... 23 2.8 The diffractometer ...... 25 2.9 The UHV-baby chamber ...... 26 2.10 (a) UHV-baby chamber mounted at the ESCA-lab (b) UHV-baby chamber mounted on the diffractometer ...... 27 2.11 Typical measurement setup ...... 28

3.1 Typical STM setup ...... 39

4.1 The Ru(0001)-surface ...... 45 4.2 The Rh(111)-surface ...... 45 4.3 The sp2-hybridization ...... 47 4.4 (a) The sp2-hybridized layer in real space (b) The sp2-hybridized layer in recip- rocal space ...... 48 4.5 Moir´epattern ...... 48 4.6 The stacking of h-BN crystals ...... 49

–xvii– xviii LIST OF FIGURES

4.7 Density of states of the nanomesh h-BN/Rh(111) ...... 50 4.8 The Bernal stacking of graphite ...... 51 4.9 a) The dispersion relation of freestanding graphene b) The dispersion relation of graphene, when coupled to the substrate...... 53 4.10 Superstructure and intensity distribution in reciprocal space ...... 56 Chapter 1

Introduction

Parallel developments of nanomaterials and synchrotron radiation technology worldwide over the last decades have been particularly rapid. New advances in the theoretical background as well as in experimental methods are responsible for this development, which has had an impact on both, fundamental research and industrial and technological applications.

When the nanometer size range is approached, the physical properties of a material can change dramatically. The bulk properties of any material are merely the average of all the quantum forces affecting the atoms. As one scales down to ever smaller dimensions, this aver- aging breaks down. There are two main reasons for this: first is the increased surface-area-to- volume ratio, which means a large fraction of the atoms are at a surface, where rearrangements of electron orbitals will occur, which would otherwise be involved in boding in the bulk, thus affecting the electronic properties. Second are quantum finite size effects which occur as di- mensions approach that of the Bloch waves in the material. These can begin to dominate the behaviour of matter at the nanoscale and are the reasons why nanotechnology and nanoscience are so intensely researched.

One of the most striking developments in nanoscale science analysis was realized by the invention of the scanning tunneling microscope (STM) in 1982 [1], followed by the invention of the atomic force microscope (AFM) [2]. The STM and AFM have provided revolutionary tools for the nanoscopic investigation of the morphology and structural modification of these surfaces

–1– 2 INTRODUCTION

down to atomic scales. These techniques probe the surface very locally with high resolution, but do provide little or no depth information. Low-energy electron-diffraction (LEED) is a technique, which does provide long range order information, and the strong interaction of electrons with matter imbues it with a high sensitivity to the topmost layer, but limits its the depth sensitivity to only a few monolayers. Very often the structural changes at a surface may in fact extend down to several monolayers, depending on the nature and strength of the bonds. Indeed, a surface from the perspective of a materials scientist is not merely the topmost atomic layer, but consists of all layers which deviate significantly in their structure from that of the bulk.

X-rays, in contrast to electrons, interact weakly with matter, and can therefore give depth information. But because the scattering intensity is very low, synchrotrons were the key feature in order to get surface x-ray diffraction (SXRD) becoming a powerful tool in the investigation of surface structures.

Synchrotrons provide sufficient flux and brilliance to obtain enough scattering intensity even from the very few scattering atoms associated with the surface region. The Swiss Light Source(SLS) is a 3rd generation synchrotron source, located at the Paul Scherrer Institut (PSI). The work described in this thesis was mainly performed at the SXRD-station of the Materials Science beamline [3], which is equipped with a (2 + 3) circle diffractometer and a 2-D single- photon-counting PILATUS 100k detector [4].

The sp2-hybridized materials hexagonal boron nitride and graphene both form commensu- rate superstructures when grown on certain transition metal substrates [5, 6, 7, 8]. The size of the superstructure periodicity of the order of 3 nm makes these honeycomblike systems very interesting from a technological point of view, since they can serve as nanotemplates. In ad- dition, freestanding graphene has attracted enormous attention since its discovery in 2004 [9], due to its remarkable electronic properties: it is a gapless semiconductor [10]. When grown on a substrate graphene can become metallic or a band gap can be opened [11], induced by the substrate. This behaviour, attributed to the structural rearrangement of the atoms on the surface is of particular importance in terms of electronic applications. Hence, structural information of these systems is of crucial importance.

This thesis presents an SXRD-study of the commensurate superstructures, h-BN/Rh(111), 3

h-BN/Ru(0001) and graphene/Ru(0001). It is structured as follows.

In Chapter 2 a general introduction to SXRD and to the experimental setup as used for a large part of this thesis is presented. The data analysis and the algorithm used for the model refinement are described.

Chapter 3 is a very short overview of the complementary methods used for the precharac- terization of the samples.

Chapter 4 gives an introduction to the physics of the sp2-hybridized layers h-BN and graphene, including a description of their structural and electronic properties, and how they change when grown on a substrate. Some fundamental aspects of the investigation of these superstructures with SXRD are also given.

In Chapter 5 the stability of h-BN on Rh(111) nanomesh under ambient conditions has been demonstrated. Beside this, a confirmation of the 13-on-12 superstructure of this system is given.

Chapter 6 investigates further the h-BN on Rh(111) nanomesh. The 13-on-12 superstructure is proved to be commensurate. Further, the commensurability up to high temperatures and a non-linear expansion of the substrate’s surface region up to 200oC demonstrates a strong bonding between substrate and film.

Chapter 7 elucidates the structure of the h-BN on Ru(0001) nanomesh. Although the in- plane lattice constant of ruthenium is larger than that one of rhodium, this structure forms a surprising 14-on-13 superstructure, instead of the initially expected 13-on-12 or 12-on-11. This is explained in terms of the especially high bonding strength of h-BN to ruthenium, which helps accommodate in-plane strain by increasing the area of the superstructure that is strongly bound and therefore has a lower chemical energy.

The focus turns to graphene on Ru(0001) in Chapter 8, where a large 25-on-23 superstructure is found. Further an initial structural study was performed which from the strong oscillations formed in the SXRD superstructure rod data demonstrates a significant corrugation of the substrate caused by strong bonding of graphene to Ru.

In Chapter 9 the graphene on Ru(0001) structure was further investigated with unsurpassed 4 BIBLIOGRAPHY

detail. After parametrization of the system, the crystal truncation rods, superstructure rods and in-plane data were fit using genetic algorithms. The structure is found to show a chiral surface.

The conclusions of the thesis are given in Chapter 10.

Bibliography

[1] G. Binnig, H. Rohrer, C. Gerber, and E. Weibel: “Surface Studies by Scanning Tunneling Mi- croscopy.” Phys. Rev. Lett. 49(1), 57–61 (1982), doi:10.1103/PhysRevLett.49.57.

[2] G. Binnig, C. F. Quate, and C. Gerber: “Atomic Force Microscope.” Phys. Rev. Lett. 56(9), 930–933 (1986), doi:10.1103/PhysRevLett.56.930.

[3] B. D. Patterson, R. Abela, H. Auderset, Q. Chen, F. Fauth, F. Gozzo, G. Ingold, H. Kuhne, M. Lange, D. Maden, D. Meister, P. Pattison, T. Schmidt, B. Schmitt, C. Schulze-Briese, M. Shi, M. Stampanoni, and P. R. Willmott: “The Materials Science Beamline at the Swiss Light Source: design and realization.” Nucl. Instrum. Meth. A 540(1), 42–67 (2005), doi: 10.1016/j.nima.2004.11.018.

[4] B. Henrich, A. Bergamaschi, C. Br¨onnimann, R. Dinapoli, E. F. Eikenberry, I. Johnson, M. Kobas, P. Kraft, A. Mozzanica, and B. Schmitt: “PILATUS: A single photon counting pixel detector for X-ray applications.” Nucl. Instrum. Meth. A 607(1), 247–249 (2009), doi: 10.1016/J.Nima.2009.03.200.

[5] D. Martoccia, P. R. Willmott, T. Brugger, M. Bj¨orck, S. G¨unther, C. M. Schlep¨utz, A. Cervel- lino, S. A. Pauli, B. D. Patterson, S. Marchini, J. Wintterlin, W. Moritz, and T. Greber: “Graphene on Ru(0001): A 25×25 Supercell.” Phys. Rev. Lett. 101(12), 126102 (2008), doi: 10.1103/PhysRevLett.101.126102.

[6] D. Martoccia, M. Bj¨orck, C. M. Schlep¨utz, T. Brugger, S. A. Pauli, B. D. Patterson, T. Greber, and P. R. Willmott: “Graphene on Ru(0001): A corrugated and chiral structure.” New J. Phys. 12, 043028 (2010), doi:10.1088/1367-2630/12/4/043028.

[7] D. Martoccia, S. A. Pauli, T. Brugger, T. Greber, B. D. Patterson, and P. R. Willmott: “h−BN on Rh(111): Persistence of a commensurate 13-on-12 superstructure up to high temperatures.” Surf. Sci. 604(5-6), L9–L11 (2010), doi:10.1016/J.Susc.2009.12.016.

[8] D. Martoccia, M. Bj¨orck, C. M. Schlep¨utz, S. A. Pauli, T. Brugger, T. Greber, B. D. Patterson, and BIBLIOGRAPHY 5

P. R. Willmott: “h-BN/Ru(0001) nanomesh: A 14-on-13 superstructure with 3.5 nm periodicity.” Surf. Sci. 604(5-6), L16–L19 (2010), doi:10.1016/J.Susc.2010.01.003.

[9] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov: “Electric field effect in atomically thin carbon films.” Science 306(5296), 666–669 (2004), doi:10.1126/science.1102896.

[10] S. Reich, J. Maultzsch, C. Thomsen, and P. Ordejon: “Tight-binding description of graphene.” Phys. Rev. B 66(3), 035412 (2002), doi:10.1103/Physrevb.66.035412.

[11] S.-Y. Kwon, C. V. Cobanu, V. Petrova, V. B. Shenoy, J. Bare˜no, V. Gambin, I. Petrov, and S. Kodambaka: “Growth of Semiconducting Graphene on Palladium.” Nano Lett. (accepted) (2009), doi:10.1021/nl902140j.

Chapter 2

Surface x-ray diffraction (SXRD)

2.1 Introduction

With the accidental discovery of x-rays in 1896 [1], when R¨ontgen found that these rays would pass through the tissue of humans leaving, bones and metals, a new area in science was opened for applications ranging from determining the internal architecture of cells and other biological structures, to solving the atomic structure of large protein structures and crystals.

In 1913 Friedrich and Kn¨opping laid the first foundations for crystal structure analysis and together with the theoretical calculations provided by Laue, their results were published in 1913 [2]. By using a crystal as a diffraction grating, von Laue proved that the x-rays were waves of light with very small wavelengths. He had recorded his results photographically, showing bright spots, where diffracted x-rays happened to be in phase with each other, but he also showed a large number of spots to be missing. Diffracted beams of x-rays were expected in these directions, but did not seem to occur. Von Laue suggested that the x-rays must contain only certain wavelengths to account for the missing diffracted beams. It was William Lawrence Bragg who suggested that x-rays must be made up of a continuous spectrum of all possible wavelengths, and if this was true then the missing directions of diffraction would not be due to the characteristics of the wavelength of the x-rays, but due to some property of the crystal being examined.

–7– 8 SURFACE X-RAY DIFFRACTION (SXRD)

William Lawrence Bragg and his father William Henry Bragg published the first full struc- ture determinations by analysis of Laue diagrams, where they determined the correct lattice upon which the structure of the crystal is built [3, 4, 5, 6]. Here they also stated the well-known Bragg’s law. The x-rays would hit each plane of atoms in turn, scattering first off the surface layer, then the one below it, and so on. If the x-rays reflected off all the surfaces were in phase a very strong signal could be measured.

Throughout research institutions and industry, x-ray diffraction has become an indispens- able method for materials investigation, characterization and quality control. Example areas of application include qualitative and quantitative phase analysis, crystallography, structural relaxation determination, micro-diffraction, investigation of nano-materials and the structural analysis of surfaces.

If a bulk crystal is cut, the surface atoms often ”reconstruct”, or shift from their bulk equilibrium positions. Therefore x-rays diffracted from the surface will may have their Bragg reflections at different angles than x-rays diffracted from the bulk. Unfortunately, the volume of the surface region is much smaller than that of the bulk crystal resulting in much weaker and broader diffraction spots, hence much more powerful x-ray sources are essential in order to look at surfaces. The most powerful sources of x-rays for research purposes are synchrotron storage rings. Synchrotrons generate tunable beams of electromagnetic radiation from the far infrared to the hard x-ray regime, with fluxes and brilliances many orders of magnitude greater than those produced by laboratory-based sources. It is thanks to synchrotrons that surface x-ray diffraction (SXRD) could develop into one of the most powerful methods today in solving surface structures.

In this chapter a short introduction to the theory of bulk diffraction will be given [7, 8], and starting from the basics of Bragg’s law and the Laue conditions, the reciprocal lattice will be introduced. The diffraction intensities of an ideal crystal will be explained with the help of the convolution theorem. Then the theory of SXRD and the fundamental concept of the crystal truncation rods will be derived, again with the help of the convolution theorem. The experimental setups used throughout the whole of this thesis will round up this first chapter. 2.2 THEORY 9

2.2 Theory

Initially the use of x-rays to probe surfaces was thought to be futile. This was based on the fact that x-rays have a low scattering cross-section and hence interact very weakly with matter resulting in a deep penetration into solids. This weak interaction is on the other hand a big advantage in the theoretical description of SXRD, compared to that for low-energy electron- diffraction (LEED). Since the cross-section for elastic scattering in the case of low-energy electrons is high, electrons can be diffracted elastically several times and still be measurable, this is known as the “multiple scattering effect” and is described by dynamical theory. In contrast, the interaction of photons with the electrons of an atom is weak and the probability of multiple scattering is close to zero, hence multiple scattering effects can be neglected in SXRD, that is, SXRD satisfies “the kinematical approximation”. This makes the interpretation of an SXRD pattern fairly straightforward [9, 10, 11].

2.2.1 Bulk diffraction

2.2.1.1 Bragg’s Law

When an ideal crystal is illuminated with x-rays of a fixed wavelength, which is comparable to distances between atomic planes in a crystal, so-called Bragg-peaks are observed, whereby the x-rays interfere constructively. In order to do so, the difference of 2x in the travel path length of the diffracted x-rays (see Figure 2.1) must be equal to integer multiples of the wavelength. The general relationship between the wavelength of the incident x-rays, the incident angle and spacing between the crystal lattice planes is expressed by Bragg’s Law. With d, the spacing between two adjacent planes of atoms, λ the wavelength, θ the angle of the incident beam to the surface, and n an integer number, Bragg’s Law is expressed as

nλ = 2d sin(θ). (2.1)

Solving Bragg’s Equation gives the d-spacing between the crystal lattice planes of atoms that produce the constructive interference. A given crystal has many different planes of atoms in its structure; therefore, the collection of reflections of all the planes can be used to uniquely identify the structure of an unknown crystal. 10 SURFACE X-RAY DIFFRACTION (SXRD)

(a) (b)

Figure 2.1: (a) Bragg’s Law describes how an x-ray beam is reflected or diffracted in a crystal lattice. Bragg peaks are seen when the rays interfere constructively. (b) Zoom region: The difference in the path lengths between x-ray A and x-ray B is of 2x. Bragg’s law is fulfilled when the difference in the path length 2 · x is equal to an integer multiple of the wavelength λ.

2.2.1.2 Lattice and reciprocal lattice

Let a, b, c be the primitive vectors, hence linearly independent, of a crystal lattice. The so-called Bravais lattice is built up by all points R in real space which can be written as

R = n1a + n2b + n3c, with n1, n2, n3 ∈ Z. (2.2)

A crystal is a Bravais lattice in which associated with each lattice point is a basis which consists of physical structures such as atoms, ions and molecules.

The reciprocal lattice is spanned by the primitive vectors a∗, b∗, c∗. One can show [12] that the reciprocal lattice is the Fourier transform of the real space lattice and that the two lattices are connected to each other via the following relations:

∗ b × c a = 2π (2.3) a · (b × c)

∗ c × a b = 2π (2.4) a · (b × c)

∗ a × b c = 2π . (2.5) a · (b × c) With these vectors any point of the reciprocal lattice can be described by

∗ ∗ ∗ G = ha + kb + lc h, k, l ∈ Z (2.6) 2.2 THEORY 11

Figure 2.2: The Laue condition: Laue formulated an alternative theorem to Bragg’s law for diffraction. This theorem is beneficial because it does not require the assumptions used by Bragg, that reflection is specular and involves parallel planes of atoms. It states that the difference between incoming and scattered wavevector must be equal to a reciprocal lattice vector. and as a direct consequence of the definition of the reciprocal lattice vectors we state:

∗ xi · xj = δij x ∈ {a, b, c}. (2.7)

2.2.1.3 The Laue condition

In Figure 2.2 we see that the path length difference of the two rays diffracted from two single atoms can be expressed as

k k ∆x = i · r +(− f · r), (2.8) ki kf where r is a vector connecting two lattice points in real space, ki (= 2π/λ) is the wavevector representing an incoming plane wave and kf (|kf | = |ki|) represents the outgoing plane wave.

We will denote the difference of the two wavevectors as q = ∆k = kf − ki. Knowing already from Bragg’s law (see Section 2.2.1.1) that we only have constructive interference of two x-rays when the difference in the path length is a multiple of the wavelength, and making use of the fact that we want to detect only the elastically scattered photons, |ki| = |kf |, we get

r · q = 2π · n (2.9) 12 SURFACE X-RAY DIFFRACTION (SXRD)

Using Equation 2.7 we can directly derive the three Laue Equations:

a · q = 2πh

b · q = 2πk

c · q = 2πl. (2.10)

If G is the reciprocal lattice vector, we know from the mathematical construction of the reciprocal lattice (see Section 2.2.1.2) that G · (a + b + c) = 2π(h + k + l). The Laue equations specify q · (a + b + c) = 2π(h + k + l), hence we have

q = G. (2.11)

In other words: the difference between incoming and scattered wavevector must be equal to a reciprocal lattice vector.

2.2.1.4 The Ewald sphere construction

In 1913 Peter Ewald published details of a geometrical construction [13] interpreting the Laue conditions. When a beam hits a crystal and only elastic scattering is considered, the Ewald sphere shows which sets of planes are at their Bragg angle for diffraction to occur.

Let a crystal be depicted by its reciprocal lattice with its origin (000). We consider a plane wave with wavevector ki and with wavelength λ incident on the crystal. ki starts at the center of the Ewald sphere and ends at the origin of the reciprocal lattice. The diffracted wavevector kf has got the same length as the incident one, since we only consider elastic scattering. Hence all diffracted beams will sit on a sphere with length |ki| = 2π/λ. The difference between the wave-vectors of diffracted and incident wave is named the scattering vector ∆k = kf −ki. Since we know already that diffraction maxima can only occur when ∆k = G (Section 2.2.1.3), all the recordable reciprocal lattice points will be on the surface of the Ewald sphere, depicted in yellow in Figure 2.3. 2.2 THEORY 13

Figure 2.3: The Ewald Sphere represents all the points in reciprocal space where elastic scattering can occur. Its intercept with a diffraction pattern presents all the recordable reflections for a given wavelength λ of the x-rays. The (hkl) = (000) and (100) reflections are highlighted in yellow, as an example of an observable diffraction pattern.

2.2.1.5 The convolution theorem

The next step is to bring the basis into play. For that we will make use of the convolution theorem. Later on, some fundamental and important aspects of SXRD will be made clear also with the help of this theorem.

The convolution is a mathematical operation of two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions by the second one. The convolution of f(x) and g(x) is written as f ⊗ g and is defined as

∞ ′ ′ ′ (f ⊗ g)(x) ≡ f(x ) · g(x − x )dx (2.12) Z−∞

The convolution theorem says that “the Fourier-transform of the product of two functions, f and g, is equal to the convolution of the Fourier transform of function f and the Fourier- transform of function g”. This also works the other way round, namely “the Fourier-transform 14 SURFACE X-RAY DIFFRACTION (SXRD)

of the convolution of two functions, f and g, is equal to the product of the Fourier transform of function f and the Fourier-transform of function g”

F(f · g) = F(f) ⊗F(g) (2.13)

F(f ⊗ g) = F(f) ·F(g). (2.14)

This very important theorem will make it possible to understand how the diffraction pattern of an ideal infinite crystal and further on how the diffraction pattern of the surface of such a crystal looks like.

2.2.1.6 Diffraction from an ideal infinite crystal

We have already said that the reciprocal lattice is the Fourier transform of the real space lattice (see Section 2.2.1.2) and that in the same way the scattering amplitudes in reciprocal space are the Fourier components of the real space crystal. This fact can be derived mathematically by starting from the elastic scattering of a free electron (Thomson scattering), going over to the scattering from an atom by integrating over the whole charge distribution, which is explained in detail elsewhere [14]. For the sake of simplicity we will give here a more descriptive explanation, namely using the convolution theorem (see Section 2.2.1.5)

Since a crystal is nothing more than the convolution of the Bravais lattice with the basis, due to Equation 2.14 the Fourier transform of the crystal has to be equal to the product of the Fourier transform of the Bravais lattice and the Fourier transform of the atom (see Figure 2.4). The Fourier transform of the Bravais lattice is the reciprocal lattice (a set of δ- functions) (Section 2.2.1.2), whereas the Fourier transform of the electron density distribution is a continuous function which falls off with higher q values in reciprocal space. Since the observable intensity is proportional to the squared structure factor, squaring the product gives a reciprocal lattice with distinct intensities on the lattice points, falling off with higher q- values. 2.2 THEORY 15

(a)

(b)

Figure 2.4: (a) In real space a crystal can be mathematically expressed by the convolution of two func- tions, one representing the Bravais lattice, say f, one representing the basis, say g. (b) The convolution theorem states that the Fourier transform F of f ⊗ g is equal to the product of F(f) with F(g). The Fourier transform of the Bravais lattice is the reciprocal lattice, which consists of a set of δ-functions, whereas the Fourier transform of the basis is a continuous function which falls off with higher q values in reciprocal space. The detectable quantity is the intensity. 16 SURFACE X-RAY DIFFRACTION (SXRD)

2.2.1.7 Structure factors

The Fourier transform F of a function f(r) at a point q is defined as ∞ − F(f(r))(q) ≡ f(r) · e 2πiqrdr. (2.15) Z−∞ With this we can calculate the Fourier transform of the total electron density ρ(r) in a single atom at a scattering vector q. This quantity f(q) is also called the atomic form factor and is expressed by: ∞ − f(q)= F(ρ(r))(q)= ρ(r) · e 2πiqrdr. (2.16) Z−∞ The atomic form factors for all atoms are tabled [15] and are used whenever intensities in recip- rocal space have to be calculated. Two boundary cases may be mentioned to this expression. First we note that for the case where q = 0, f(q) becomes Z, where Z is the atomic number of the atom, hence f(q = 0) = Z. Second for q → ∞, e−2πiqr oscillates with a high frequency, such that all scattering contributions cancel out on average, hence f(q → ∞) = 0.

For the calculation of the structure factor Fuc(q), which is the scattering of an entire unit cell, one builds up the sum over all n atoms within this unit cell n −2πiqr Fuc(q)= fj(q) · e j , (2.17) Xj=1 where fj(q) are the atomic form factors or the Fourier transform of the electron density of the single atoms (see Equation 2.15 and Equation 2.16) and rj is the position of the atom within the unit cell.

2.2.1.8 Scattering from a crystal

To calculate what the structure factor of an entire crystal looks like, one just has to add up all the structure factors of the entire crystal, taking into consideration the phase difference between the scattered waves originating from two different lattice points. The position of an atom is now given by rj + Rk and by summing up over all structure factors one gets:

Fuc(q) lattice sum m n n m − − − 2πiq(rj +Rk) 2πiqrj 2πiqRk Fcrystal(q)= fj(q) · e = z fj(q)}|· e { · z e }| { . (2.18) Xk=1 Xj=1 Xj=1 Xk=1 2.2 THEORY 17

The first sum here is the structure factor Fuc (see Equation 2.17) and we will call the second term the lattice sum, which is independent of the type of atoms involved, and only depends on how the atoms are arranged within the lattice.

2.2.1.9 The lattice sum

In Section 2.2.1.8 we have seen that the total scattering factor from a crystal can be written as the product of the structure factor and the lattice sum. We focus here on the latter and calculate the lattice sum for a crystal containing n1 × n2 × n3 atoms:. m − − ∗ ∗ ∗ · S(q) = e 2πiqRk = e 2πi(ha +kb +lc ) (n1a+n2b+n3c) Xk=1 n1X,n2,n3

− − − = e 2πihn1 · e 2πikn2 · e 2πiln3 . (2.19) Xn1 Xn2 Xn3

For the summation over n1, n2, n3, from 0 to N1 −1, N2 −1, N3 −1 each of the sums corresponds to a geometrical series, which can be calculated: − N1 1 −2πihN1 −2πihn1 1 − e sin(πN1h) πi(N1−1)h Sn1 (h) = e = = · e (2.20) 1 − e−2πih sin(πh) nX1=0

− N2 1 −2πikN2 −2πikn2 1 − e sin(πN2k) πi(N2−1)k Sn2 (k) = e = = · e (2.21) 1 − e−2πik sin(πk) nX2=0

− N3 1 −2πilN3 −2πiln3 1 − e sin(πN3l) πi(N3−1)l Sn3 (l) = e = = · e (2.22) 1 − e−2πil sin(πl) nX3=0

2.2.1.10 Argand diagram

Apart from the interpretation of the squared structure factor, the structure factor itself has also a geometrical interpretation. As we have seen (see Equation 2.17), the structure factor is a complex number which can be represented by a vector in the complex plane. Scattering from individual atoms within the unit cell is represented hence by such a vector, and therefore the sum over all the complex atomic form factors in a unit cell is equivalent to the sum over all the corresponding vectors in the complex plane. This is represented in the Argand diagram (see Figure 2.5). If the positions of atoms in the unit cell are such that for a particular set of 18 SURFACE X-RAY DIFFRACTION (SXRD)

Figure 2.5: The Argand diagram is the graphical representation of the structure factor, it can be used to explain the extinction of some reflexes in reciprocal space. The complex structure factors are represented as complex number in the complex plane as vectors. The total structure factor can be calculated by adding up all the structure factors, hence building the sum over all vectors. If the resulting vector is 0 the structure factors cancel out each other and the reflex is extincted. planes (hkl) the total sum of complex vectors is zero, there will be no diffracted beam for that particular set of planes, even when the Bragg condition is satisfied. This explains the absence of some reflexes in the diffraction patterns.

2.2.1.11 Intensity and the phase problem

As mentioned already the detectable quantity is the intensity and not the structure factor itself. The intensity is proportional to the squared structure factor

∗ 2 2 2 Icrystal(q) ∝ |Fcrystal(q) · Fcrystal(q)| ∝|Fcrystal(q)| ∝|Sn1 (h) · Sn2 (k) · Sn3 (l)|

sin(πN h) 2 sin(πN k) 2 sin(πN l) 2 = 1 · 2 · 3 , (2.23)  sin(πh)   sin(πk)   sin(πl) 

∗ where Fcrystal(q) is the complex conjugation of Fcrystal(q). Here we also directly see the problem arising when we measure integrated intensities in an experiment. What we would like to measure is the complex structure factors Fuc(q), but there is no way of doing this. Instead we measure the intensities, which is the square of the structure factors, but by squaring the structure factor we lose the phase information. This is known as the phase problem. 2.2 THEORY 19

2.2.2 Diffraction from a surface

2.2.2.1 Crystal truncation rods

We introduce now the concept of a crystal truncation rod (CTR), first detailed by I. K. Robinson in 1986 [9], where we will again make use of the mathematical description of the convolution theorem (see Section 2.2.1.5).

One can consider a crystalline surface an infinitely extended crystal which is truncated by an ideal 2-dimensional plane (see Figure 2.6(a)). Mathematically this is expressed by the product of two functions, one standing for the crystal, say f, one representing the truncating plane, g. The Fourier transform of the product of these two functions hence is, due to the convolution theorem (Equation 2.14), equal to the convolution of the Fourier transform of f and the Fourier-transform of g (see Figure 2.6(b)). The Fourier transform of g is proportional to 1/qz if the surface normal is pointing in z-direction. So, the presence of a surface in real space will smear out the δ-functions in the direction of the surface normal. The result is to add 2 a 1/qz intensity tail to each bulk peak along the direction of the surface normal, which, in our coordinate frame, is the direction spanned by the index L. The bulk Bragg peaks will be aligned in linear arrays and these tails join them together to form continuous ridges of diffraction, the so-called Crystal Truncation Rods (CTR), extending all the way through reciprocal space, as illustrated in Figure 2.6(b).

2.2.2.2 Structure factor of a surface

We have seen in Section 2.2.1.8 what the structure factor of an infinite crystal is. Using the same approach we now want to derive what the structure factor of a surface looks like. Starting from Equation 2.18 we know that the structure factor for an infinitely extended crystal is the product of the unit cell structure factor Fuc(q) times the lattice sum. Here we want to calculate the structure factor along the CTR, hence we only have to consider the direction perpendicular to the surface, z, since the lattice sums of the in-plane directions are not influenced by the introduction of a surface. 20 SURFACE X-RAY DIFFRACTION (SXRD)

(a)

(b)

Figure 2.6: (a) A crystal surface can be represented by the product of a function, say f, representing the crystal and a function representing the surface, say g. (b) Due to the convolution theorem the Fourier transform the crystal surface is the product of the Fourier transform of the crystal convoluted with the Fourier transform of the surface. This gives rise to the CTRs.

The lattice sum as introduced in Section 2.2.1.9 turns then into

∞ − 1 S (l)= e 2πiln3 = . (2.24) CTR 1 − e−2πil Xk=0 2.2 THEORY 21

2.2.2.3 Intensity

The measurable intensity is proportional to the squared structure factor, so by using Equa- tion 2.18 we obtain

2 2 Isurface(q) ∝|Fsurface(q)| ∝ |Sn1 (h) · Sn2 (k) · Sn3 (l)| (2.25) sin(πN h) sin(πN k) 1 = 1 · 2 · (2.26) sin(πh) sin(πk) 4π sin2 (πl) Here again as in Section 2.2.1.11 by squaring the structure factor we lose the phase information. In recent years several phase retrieval methods for SXRD have been proposed [16, 17, 18, 19]. They have been proven to work for relatively simple systems [20, 21, 22] but they are still in a developing stage. For the more complicated systems such as structures including reconstructions, fitting methods are indispensable.

2.2.2.4 Debye-Waller factor and occupation

In general there are two more factors which will change the structure factor Fuc(q) and so influence the intensity of a CTR. First the so called Debye-Waller Factor (DWF), is used to describe the attenuation of x-ray scattering by thermal motion of the atoms. It is defined as

B − 1 t j 2 q 2 q Dj ≡ e 8π (2.27)

2 where Bj/(8π ) is a (3×3) symmetric matrix, called the Dispersion Matrix. In a simplified case where we assume the DWF to be isotropic we can define the root mean-square-displacement of an atom j as

Bj σj = . (2.28) r8π2 The second parameter to be mentioned is the occupation parameter, which is used to describe partially occupied atom sites, here denoted as Θj. It can assume values between 0 and 1. The unit cell structure factor is newly written as

n −2πiqr Fuc(q)=Θj · Dj · fj(q) · e j (2.29) Xj=1 22 SURFACE X-RAY DIFFRACTION (SXRD)

2.2.2.5 Superstructure rods

Atoms at the surface of a crystal often assume a different structure than that of the bulk, this is called a surface reconstruction. This structural changes will alter the physical properties of the surface compared to the bulk. Surface reconstructions are also important in that they help in the understanding of surface chemistry for various materials, especially in the case where a different material is adsorbed at the surface.

In an ideal infinite crystal, the equilibrium position of each individual atom is determined by the forces acting by all the other crystal atoms, resulting in a periodic structure. If a surface is introduced to the system, these forces are different and hence they change the equilibrium positions of the atoms. It is most noticeable for the atoms in the surface region, as they now experience no inter-atomic forces from above the structure. This imbalance results in the atoms near the surface assuming positions with different spacing and symmetry from the bulk atoms, creating a different surface structure than present in the bulk material. Often the periodicity of the surface structure is bigger in the surface plane than the one of the bulk structure and hence this will be expressed in the diffraction pattern by the appearance of new CTRs, which in this case are called “superstructure rods” (SSRs), since they originate from a superstructure.

Because SSRs arise from rearrangements only in the surface region, SSRs do not have the intense Bragg peaks associated with bulk diffraction that one finds in CTRs. Instead, SSRs have intensities that remain comparable to those found at the weakest positions of CTRs, due to the relatively small number of scatterers involved.

2.3 Experimental Setup

2.3.1 The Materials Science beamline

A detailed description of the Materials Science Beamline at the SLS can be found elsewhere [23, 24].

The Materials Science Beamline at the SLS produces hard x-rays in the photon-energy range 5 − 40 keV employing in the present setup a “minigap wiggler” as the insertion device. After 2.3 EXPERIMENTAL SETUP 23

insertion device

beam−defining aperture

soft x−ray filter/window beam−defining slits

beam intensity focussing and monitor detector monochromator optics

clean−up slits

secondary optics sample

Figure 2.7: A typical beamline setup, as it is found also at the Materials Science beamline, SLS, PSI. When electrons pass through an insertion device, in this case an undulator or a wiggler, a strong photon source is produced. After having passed some optics elements, the monochromator selects the energy by changing the Bragg angle. The beam hits the sample and is diffracted, and the diffracted intensities are recorded with the 2D PILATUS 100k detector. the x-ray beam has passed the beam defining apertures, it hits a rotating carbon filter, which acts as a high band pass filter for energies below 5 keV. This is important since photons in this energy range interact strongly with material and would destroy sensitive components of the beamline. Because carbon can stand high temperatures and has a good thermal conductivity, it is optimally suited for this component. After a set of beam-defining slits the beam hits the double crystal monochromator, which is enclosed by two mirrors, both needed for vertical focussing of the beam. The first crystal is responsible for the energy selection and for the horizontal focussing, whereby the second one provides a constant height of the beam entering the experimental hutch.

2.3.2 The diffractometer

There can be found a lot of literature regarding different types of diffractometer and angle calculations [25, 26, 27, 28, 29, 30]. Here we describe the surface diffractometer (Micro-Controle Newport, France) used for SXRD-measurements at the Materials Science beamline, Swiss Light 24 SURFACE X-RAY DIFFRACTION (SXRD)

Source, Paul Scherrer Institut. It is a so-called (2 + 3)-circle diffractometer, which means 2 circles act for the sample movement and 3 circles for the detector movement. The diffractometer can be run either in vertical or in horizontal geometry. In the vertical geometry, used throughout all the present experiments, the sample circles are α and ωv (see Figure 2.8), where α denotes the incoming angle of the x-rays with respect to the sample surface and ωv is the rotation of the sample around its surface normal. The detector circles for horizontal and vertical geometry are the same, namely γ, δ and ν. γ stands for the rotation around the vertical direction which is the normal to the base plane of the diffractometer, which itself can be adjusted to be perfectly horizontal by Y1,Y2 and Y3. δ describes the polar angle. ν is the rotation of the detector around its normal axis. In a horizontal geometry the sample rotations are represented by φ and ωh (see Figure 2.8). The hexapod is based on six high-resolution actuators that control the platform and hence the sample surface with 3 translational and 3 rotational degrees of freedom. It can be mounted in horizontal and vertical geometry and the chambers can be directly fixed to it. The detailed calculations of the coordinate transformations from real to reciprocal space applied to this specific kind of diffractometer can be found in [31, 32].

2.3.3 UHV-baby chamber

For obtaining the structural information of well-prepared surfaces it is very important to provide and maintain a very well-defined state of the surface. For this purpose high-quality surfaces can often only be prepared using ultrahigh vacuum (UHV) techniques. Exposures of well- prepared surfaces to ambient air, containing oxygen and other reactive components will often result in a change of the surface structure. To avoid this, the goal is to prepare and measure the surface structure without having to break the vacuum. Since preparation and measure- ments often take place at different locations, as it was for the experiments here presented, the motivation was to design and build a transportable UHV-baby chamber specially suited for SXRD-measurements [see Figure 2.9(a)]. This approach enables one to combine not only the growth of samples with the SXRD-measurements, but also to use different surface analysis tools for pre-characterization of the surface structure, such as scanning tunneling microscopy (STM), low-energy electron-spectroscopy (LEED), x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), x-ray photoelectron diffraction (XPD), which usually are 2.3 EXPERIMENTAL SETUP 25

pixel

$ rays "v x−

% DC 1385 mm

hexapod '

"h

Y1 Xv & Y2

Y # 3

TRX

!v

Figure 2.8: The diffractometer as it is found at the Surface Diffraction station of the Materials Science beamline, SLS, PSI. It is a (2 + 3)-circle diffractometer, 2 motors regard the sample movement, 3 are used for positioning the detector. It is equipped with a hexapod, which controls the alignment of the sample with micrometer-accuracy. not provided at an SXRD-beamline. For the present work all pre-characterizations of the sam- ples were done at the ESCA-Lab of the Physik Institut, Unviversi¨atZ¨urich, Switzerland. For the transfer the chamber is connected via a DN40CF UHV flange to a tee connector attached to a docking port of the larger UHV chamber (see Figure 2.10(a)). A Varian VacIon Plus 20 pump allows one to maintain good UHV conditions (pressure of better than 2 × 10−9 mbar). A cold cathode ion gauge tracks the pressure inside the chamber. Two 12 V batteries provide the power during transport and last (depending on the pressure) usually more than 20 hours. The whole chamber can be directly mounted to the hexapod (see Figure 2.10(b)). The hemi- spherical beryllium dome (Brush Wellman Inc.) acts as an x-ray window allowing for the entry of x-rays. It has an inner radius of 31.5 mm and a thickness of 0.4 mm. The sample holder 26 SURFACE X-RAY DIFFRACTION (SXRD)

Figure 2.9: Schematic drawing of the UHV-baby chamber. It is equipped with an x-ray transparent beryllium dome, an ion pump assuring pressures below 2 × 10−9 mbar, a pressure gauge, a manipulator for fixing the sample holder within the chamber and a battery supply of 2 × 12 V. The chamber can transfer samples via a DN40CF flange. It ensures UHV-conditions during sample transport for more than 20 hours and can be directly mounted on the diffractometer at the SXRD-station of the Materials Science beamline, SLS. mechanism can accommodate our standard sample holder (see Figure 2.9), Swiss Stubs and allows to heat the sample to temperatures of at least 900oC. A 600 mm transfer arm allows to pick up the sample at distances up to 400 mm away from the gate valve. The design of the chamber basis on [33].

2.3.4 The PILATUS 100k detector

In SXRD-experiments one often has to deal with weak signals originating from the topmost reconstructed layers of the investigated surface. To achieve the best possible signal quality detectors with a large dynamic range, high count-rate capability, low dark noise and fast read- out times are required. This is what the here used detector was designed and developed for. 2.3 EXPERIMENTAL SETUP 27

(a) (b)

Figure 2.10: (a) The UHV-baby chamber mounted at the ESCA-lab at the Physik-Institut, Universit¨at Z¨urich. It is attached to the load-lock via a DN40CF flange and the long transfer arm transfers the sample from the main chamber to the UHV-baby chamber. (b) The UHV-baby chamber can be mounted on the diffractometer at the surface diffraction station of the Materials Science beamline, SLS, PSI. The beryllium dome ensures the transparency for x-rays.

The PILATUS 100k detector is a single photon counting pixel detector for x-ray applications. It relies on the hybrid pixel technology combining silicon sensors with complementary metal oxide semiconductor (CMOS) technology. It was developed at the Paul Scherrer Institut and was first used at the Surface Diffraction station of the Material Science beamline, SLS. It consists of 487 × 195 = 94965 pixels in total each with a pixel size is (172 × 172) µm [34, 35, 36]. Each pixel hence covers an angle of (0.0086 × 0.0086)o taking into account that the distance of the detector to the center of the diffractometer is 1141 mm. The total angular acceptance of the whole detector at this distance is (4.2 × 1.7)o, which ensures that the whole signal can be captured in a single shot and gives visual feedback in discriminating signal from artifact- features. 28 SURFACE X-RAY DIFFRACTION (SXRD)

Figure 2.11: A typical measurement setup with a PILATUS 100k detector image taken on the (11)- CTR on graphene/Ru(0001) at l = 1.5. The whole signal, which is the intercept of the CTR with the Ewald sphere fits on the detector due to the large subtended angle of the detector.

2.4 Data recording, extraction and correction

Traditionally SXRD-data is recorded by performing so called rocking scans [27]. A measure- ment of the diffracted intensity is done by holding fixed the detector relative to the incident beam, while rotating, or “rocking” the sample. Nowadays using the new 2D-detectors there is also another way of recording data. Here one can measure the integrated intensity for one l-value in one single shot. In this section we will briefly describe the different modes to record data, the extraction and correction of it as they were used for the present work. A visualization of a typical measurement setup is given in Figure 2.11. The detected signal on the detector is given by the intersection of the Ewald Sphere with the CTR. 2.4 DATA RECORDING, EXTRACTION AND CORRECTION 29

2.4.1 Rocking scan

In a standard SXRD-experiment the rocking scans are performed by first orienting the sample and the detector to fulfill the diffraction condition and then rotating the sample at positive and negative ωv-values around its surface normal. During the rotation of the sample, the detector positions are kept fixed. The integrated intensity at each l-value of a CTR is then extracted by integrating the whole rocking curve for each l-value, after having subtracted the background. Using a 2D-detector the advantage is that one can choose ∆s, the sampled l-section by setting a region of interest and integrate the signal inside it for each point of the rocking scan.

2.4.2 Stationary mode

When using a 2D-detector, instead of taking rocking scans for each l-value it is possible to catch the whole integrated intensity in a single image. One orients the sample and the detector to fulfill the desired diffraction condition and takes one image representing a certain l-value, then one moves to the next point along the l-direction [27]. In principle there are two ways of performing a scan along the l-direction. Either one can rotate the sample around its sur- face normal and readjusts the detector angles to match up the Bragg condition, or one just changes the radius of the Ewald sphere by tuning the energy (this is done in LEED). Since the definition and alignment of the beam have to be redone for every energy, which would result in aligning the sample at every l-step, rotating the sample is much more straightforward in SXRD-measurements (see Figure 2.11).

2.4.2.1 Limitations of the stationary mode

Although the stationary mode in comparison to the rocking scan mode is the much faster way of recording data, there are some limitations to it. When the Ewald sphere intercepts with the CTR (see Figure 2.11) what we see on the detector is not only one exact l-value, but a range of l-values, which we will call ∆s. Now, if we integrate the picture and read out the integrated intensity, first we have to be aware that depending on where the Ewald sphere cuts the CTR 30 SURFACE X-RAY DIFFRACTION (SXRD)

this range is different. It can be seen, that 1 ∆s ∝ , (2.30) sin(βout) where βout denotes the angle between the outgoing x-ray wavevector kf and the sample surface (see Figure 2.11). It can be calculated [31] that

sin(βout) = cos (δ) · sin(γ − βin) (2.31)

Second as we see in Figure 2.11 we have to make sure that the sampled l-section is smaller than the desired resolution ∆l, so ∆s ≤ ∆l. This is achieved by having good crystal quality and by using the stationary mode only above a critical βoutcrit . A good sample quality with large terraces results, according to the Scherrer equation, in much thinner CTRs, and hence in a smaller sampled ∆s. Another disadvantage of the stationary mode is in the case of a bad crystal quality, where scattered intensities from impurities or small crystallites inside the crystal can be found within the region of interest which one carefully selects for each image. When recording one image per l-value, this structure factor will be missing for the data analysis. When performing a rocking scan, the curve can still be interpolated. Mainly because of the last reason all SSRs within this work have been recorded performing the more reliable but much slower rocking scans.

2.4.3 h- or k- scan

In order to measure the precise size of superstructures (see Chapter 5, 8, 9, 6, 7), scans along the reciprocal directions h or k should be done. These scans are very similar to rocking scans, although, since we are not scanning perpendicular to the tangential of the Ewald sphere, as it is done in a rocking scan, one has to move also the detector to match up the correct diffraction conditions. This means that the correction factors will be slightly different (see Section 2.4.4).

2.4.4 Extraction and correction

The CTR- and SSR- data has been extracted and corrected using standard procedures, which are described elsewhere [28, 32, 37]. There is only one point which has to be mentioned: We 2.5 FITTING USING GENETIC ALGORITHMS 31

have seen, that during an h- or k-scans one moves the detector motors δ and γ, in contrast to the classical rocking scan. This means that in contrast to a classical rocking scan, where all correction factors stay constant over one scan (in the case of a round sample), here the correction factors have to be applied to each point of the scan individually.

2.5 Fitting using Genetic Algorithms

Although SXRD is a powerful method for solving surface structures, it still suffers from the phase problem, as discussed in Section 2.2.1.11. One can attempt to resolve this problem either by using the so-called direct methods [18, 19, 38, 39, 40, 41], where iterative algorithms retrieve the phase, or by using classical model fitting. In order to use phase-retrieval algorithms one requires large datasets, ideally complete datasets, whereby all the structure factors accessible within the Ewald sphere are collected.

In comparison to “normal” XRD, where a complete dataset can be recorded fairly quickly, a complete dataset in SXRD can be much larger due to the breaking of the symmetry along the third dimension. Recording a complete dataset of a non-reconstructed surface typically requires two days. Of course this depends on the sample quality, symmetry of the sample, the detector, and diffractometer type. When the surface is reconstructed and superstructure rods arise, the time needed for recording such a dataset increases accordingly, especially if there are many superstructure rods as it is the case in the present work, recording a complete dataset becomes impossible.

Therefore the method used for solving the structure in Chapter 9 was model fitting. In model fitting the goal is to reach the global minimum of differences between the simulation and the recorded data. In the systems presented in this thesis, the number of contributing atoms is so large that one has to parametrize the structure as a single periodic deviation from an ideal flat starting structure using Fourier components.

Depending on the number of parameters involved, the “landscape” can be highly compli- cated. The choice of parametrization is critical in obtaining the correct final structure. This is why complementary experimental methods, such as STM, LEED and UPS are so important 32 SURFACE X-RAY DIFFRACTION (SXRD)

in this respect.

Once the parametrization has been defined, the central effort is to find the so called global minimum of the landscape, since this will represent the best fit and hence the structure which best reflects the experimental data. Often the number of parameters involved in this fitting procedure is large and fitting the data is time-consuming, especially in the case of large unit cells. Also here the importance of complementary methods has to be stressed, since the maxi- mum of additional information reduces the necessary size of parameter space. But even for a modest parameter space, the global minimum is usually only found when the starting model is close to the correct solution. Classical fitting techniques include the Downhill simplex [42] and the Levenberg-Marquardt [43, 44] methods, but these are unable to escape from local minima, and both therefore require fairly good estimates for the initial guess in order to find the correct minimum. The Monte Carlo Method and the Simulated Annealing are only two of several more methods, which can be applied to find the correct minimum.

For the present work a so-called genetic algorithm named GenX [45] was used, which takes its name and functionality from the evolution of biological systems in nature. Every iteration is called a generation. Generation after generation, a population adapts itself to the environment by selecting the best suited individuals according to a certain criterion. The system evolves thanks to the recombination of the genes from the previous generation and random mutation in each generation. Mutations guarantee the diversity of the population, which lends the necessary randomness to the system, while gene recombination helps to concentrate the search in the most promising regions of the parameter space, as only the genes (parameters) which are closest to the experiment (these are the best suited individuals) are allowed to recombine for the next generation. BIBLIOGRAPHY 33

Bibliography

[1] W. C. R¨ontgen: “On a New Kind of Rays.” Nature 53(1369), 274–276 (1896), doi: 10.1038/053274b0.

[2] W. Friedrich, P. Knipping, and M. Laue: “Interferenzerscheinungen bei R¨ontgenstrahlen.” Ann. Phys. 41(10), 971–988 (1913), doi:10.1002/andp.19133461004.

[3] W. H. Bragg and W. L. Bragg: “The reflection of X-rays by crystals.” P. R. Soc. Lond. A-Conta. 88(605), 428–438 (1913), doi:10.1098/rspa.1913.0040.

[4] W. H. Bragg and W. L. Bragg: “The structure of the diamond.” Nature 91, 557–557 (1913), doi:10.1098/rspa.1913.0084.

[5] W. L. Bragg: “The structure of some crystals as indicated by their diffraction of x-rays.” P. R. Soc. Lond. A-Conta. 89(610), 248–277 (1913), doi:10.1098/rspa.1913.0083.

[6] W. L. Bragg: “The specular reflection of X rays.” Nature 90, 410–410 (1913), doi: 10.1038/090410b0.

[7] J. M. Cowley: Diffraction physics. Elsevier Science B.V., Amsterdam, The Netherlands, third edition (1995).

[8] B. E. Warren: X-ray diffraction. Addison-Wesley Publishing Company, Massachusetts (1969).

[9] I. K. Robinson: “Crystal Truncation Rods and Surface-Roughness.” Phys. Rev. B 33(6), 3830–3836 (1986), doi:10.1103/PhysRevB.33.3830.

[10] R. Feidenhans’l: “Surface structure determination by X-ray diffraction.” Surf. Sci. Rep. 10(3), 105–188 (1989), doi:10.1016/0167-5729(89)90002-2.

[11] I. K. Robinson: “Surface Crystallography.” In Handbook on Synchrotron Radiation, Vol. 3, Edited by G. Brown and D. E. Moncton, 221–266, Amsterdam, North-Holland, third edition (1991).

[12] C. Kittel: Introduction to Solid State Physics. John Wiley & Sons Inc., New York, fifth edition (1976).

[13] P. P. Ewald: “Zur Theorie der Interferenzen der Ro¨ntgentstrahlen in Kristallen.” Physikalische Zeitschrift 14, 465–472 (1913).

[14] J. D. Jackson: Classical Electrodynamics. John Wiley & Sons Inc., New York, second edition (1975). 34 BIBLIOGRAPHY

[15] E. Prince (Editor): International Tables for Crystallography, Vol. C, Mathematical, physical and chemical tables. International Union of Crystallography, Chester, first online edition (2006), doi: 10.1107/97809553602060000001.

[16] J. Rius, C. Miravitlles, and R. Allmann: “A Tangent Formula Derived from Patterson-Function Arguments. IV. The Solution of Difference Structures Directly from Superstructure Reflections.” Acta Crystallogr. Sect. E 52(4), 634 (1996), doi:10.1107/s0108767396003285.

[17] Y. Yacoby, R. Pindak, R. MacHarrie, L. Pfeiffer, L. Berman, and R. Clarke: “Direct structure determination of systems with two-dimensional periodicity.” J. Phys. Condens. Matter 12(17), 3929–3938 (2000), doi:10.1088/0953-8984/12/17/301.

[18] D. K. Saldin, R. J. Harder, V. L. Shneerson, and W. Moritz: “Phase retrieval methods for sur- face x-ray diffraction.” J. Phys. Condens. Matter 13(47), 10689–10707 (2001), doi:10.1088/0953- 8984/13/47/311.

[19] M. Bj¨orck, C. M. Schlep¨utz, S. A. Pauli, D. Martoccia, R. Herger, and P. R. Willmott: “Atomic imaging of thin films with surface x-ray diffraction: introducing DCAF.” J. Phys. Condens. Matter 20(44), 445006 (2008), doi:10.1088/0953-8984/20/44/445006.

[20] P. R. Willmott, S. A. Pauli, R. Herger, C. M. Schlep¨utz, D. Martoccia, B. D. Patterson, B. Delley, R. Clarke, D. Kumah, C. Cionca, and Y. Yacoby: “Structural basis for the con-

ducting interface between LaAlO3 and SrTiO3.” Phys. Rev. Lett. 99(15), 155502 (2007), doi: 10.1103/PhysRevLett.99.155502.

[21] R. Herger, P. R. Willmott, C. M. Schlep¨utz, M. Bj¨orck, S. A. Pauli, D. Martoccia, B. D. Patterson, D. Kumah, R. Clarke, Y. Yacoby, and M. Dobeli: “Structure determination of monolayer-by-

monolayer grown La1−xSrxMnO3 thin films and the onset of magnetoresistance.” Phys. Rev. B 77(8), 085401 (2008), doi:10.1103/PhysRevB.77.085401.

[22] D. P. Kumah, S. Shusterman, Y. Paltiel, Y. Yacoby, and R. Clarke: “Atomic-scale mapping of quantum dots formed by droplet epitaxy.” Nat. Nanotechnol. (2009), doi:10.1038/nnano.2009.271.

[23] B. D. Patterson, R. Abela, H. Auderset, Q. Chen, F. Fauth, F. Gozzo, G. Ingold, H. Kuhne, M. Lange, D. Maden, D. Meister, P. Pattison, T. Schmidt, B. Schmitt, C. Schulze-Briese, M. Shi, M. Stampanoni, and P. R. Willmott: “The Materials Science Beamline at the Swiss Light Source: design and realization.” Nucl. Instrum. Meth. A 540(1), 42–67 (2005), doi: 10.1016/j.nima.2004.11.018.

[24] B. D. Patterson, C. Br¨onnimann, D. Maden, F. Gozzo, A. Groso, B. Schmitt, M. Stampanoni, and BIBLIOGRAPHY 35

P. R. Willmott: “The materials science beamline at the Swiss Light Source.” Nucl. Instrum. Meth. B 238(1-4), 224–228 (2005), doi:10.1016/j.nimb.2005.06.194.

[25] W. R. Busing and H. A. Levy: “Angle Calculations for 3- and 4- Circle X-Ray and Neutron Diffractometers.” Acta Crystallogr. 22, 457 (1967), doi:10.1107/S0365110X67000970.

[26] K. W. Evans-Lutterodt and M. T. Tang: “Angle Calculations for a 2 + 2 Surface X-Ray Diffrac- tometer.” J. Appl. Crystallogr. 28, 318–326 (1995), doi:10.1107/S0021889894011131.

[27] E. Vlieg: “Integrated Intensities Using a Six-Circle Surface X-ray Diffractometer.” J. Appl. Crys- tallogr. 30(5), 532 (1997), doi:10.1107/s0021889897002537.

[28] E. Vlieg: “A (2+3)-type surface diffractometer: Mergence of the z-axis and (2+2)-type geometries.” J. Appl. Crystallogr. 31, 198–203 (1998), doi:10.1107/S0021889897009990.

[29] H. You: “Angle calculations for a 4S+2D’ six-circle diffractometer.” J. Appl. Crystallogr. 32, 614– 623 (1999), doi:10.1107/S0021889899001223.

[30] O. Bunk and M. M. Nielsen: “Angle calculations for a z-axis/(2S+2D) hybrid diffractometer.” J. Appl. Crystallogr. 37, 216–222 (2004), doi:10.1107/S0021889803029686.

[31] P. R. Willmott and C. M. Schlep¨utz: “Angle calculations for the 5-circle surface diffractometer of the Materials Science beamline at the Swiss Light Source.” (2007). URL http://sls.web.psi.ch/view.php/beamlines/ms/sd/primer/anglecalculations.pdf

[32] C. M. Schlep¨utz: Systematic Structure Investigation of YBCO Thin Films with Direct Methods and Surface X-ray Diffraction. Ph.D. thesis, University of Zurich (2009).

[33] F. U. Renner, Y. Grunder, and J. Zegenhagen: “Portable chamber for the study of UHV prepared electrochemical interfaces by hard x-ray diffraction.” Rev. Sci. Instrum. 78(3), 033903 (2007), doi: 10.1063/1.2714046.

[34] B. Henrich, A. Bergamaschi, C. Br¨onnimann, R. Dinapoli, E. F. Eikenberry, I. Johnson, M. Kobas, P. Kraft, A. Mozzanica, and B. Schmitt: “PILATUS: A single photon counting pixel detector for X-ray applications.” Nucl. Instrum. Meth. A 607(1), 247–249 (2009), doi: 10.1016/J.Nima.2009.03.200.

[35] P. Kraft, A. Bergamaschi, C. Br¨onnimann, R. Dinapoli, E. F. Eikenberry, B. Henrich, I. John- son, A. Mozzanica, C. M. Schlep¨utz, P. R. Willmott, and B. Schmitt: “Performance of single- photon-counting PILATUS detector modules.” J. Synchrotron Radiat. 16, 368–375 (2009), doi: 10.1107/S0909049509009911. 36 BIBLIOGRAPHY

[36] P. Kraft, A. Bergamaschi, C. Br¨onnimann, R. Dinapoli, E. F. Eikenberry, H. Graafsma, B. Hen- rich, I. Johnson, M. Kobas, A. Mozzanica, C. A. Schlep¨utz, and B. Schmitt: “Characterization and Calibration of PILATUS Detectors.” IEEE Trans. Nucl. Sci. 56(3), 758–764 (2009), doi: 10.1109/Tns.2008.2009448.

[37] C. M. Schlep¨utz, R. Herger, P. R. Willmott, B. D. Patterson, O. Bunk, C. Br¨onnimann, B. Hen- rich, G. Hulsen, and E. F. Eikenberry: “Improved data acquisition in grazing-incidence X-ray scattering experiments using a pixel detector.” Acta Crystallogr. Sect. E 61, 418–425 (2005), doi: 10.1107/S0108767305014790.

[38] X. Torrelles, J. Rius, F. Boscherini, S. Heun, B. H. Mueller, S. Ferrer, J. Alvarez, and C. Mirav- itlles: “Application of x-ray direct methods to surface reconstructions: The solution of projected superstructures.” Phys. Rev. B 57(8), 4281 (1998), doi:10.1103/physrevb.57.r4281.

[39] X. Torrelles, J. Rius, C. Miravitlles, and S. Ferrer: “Application of the direct methods differ- ence sum function to the solution of reconstructed surfaces.” Surf. Sci. 423(2-3), 338 (1999), doi:10.1016/s0039-6028(98)00928-5.

[40] Y. Yacoby, M. Sowwan, E. Stern, J. O. Cross, D. Brewe, R. Pindak, J. Pitney, E. M. Dufresne,

and R. Clarke: “Direct determination of epitaxial interface structure in Gd2O3 passivation on GaAs(100).” Nat. Mater. 1(2), 99–101 (2002), doi:10.1038/Nmat735.

[41] L. D. Marks, N. Erdman, and A. Subramanian: “Crystallographic direct methods for surfaces.” J. Phys. Condens. Matter 13(47), 10677–10687 (2001), doi:10.1088/0953-8984/13/47/310.

[42] J. A. Nelder and R. Mead: “A Simplex-Method for Function Minimization.” Comput. J. 7(4), 308–313 (1965), doi:10.1093/comjnl/7.4.308.

[43] K. Levenberg: “A Method for the Solution of Certain Non-Linear Problems in Least Squares.” Quart. Appl. Math. 2 164168. (1944).

[44] D. W. Marquardt: “An Algorithm for Least-Squares Estimation of Nonlinear Parameters.” Journal of the Society for Industrial and Applied Mathematics 11(2), 431–441 (1963), doi:10.1137/0111030.

[45] M. Bj¨orck and G. Andersson: “GenX: an extensible X-ray reflectivity refinement pro- gram utilizing differential evolution.” J. Appl. Crystallogr. 40(6), 1174–1178 (2007), doi: 10.1107/S0021889807045086. Chapter 3

Complementary methods

3.1 Introduction

The history of surface science hails back to the beginning of the 20th century with the discovery of the Haber process. In the intervening century many new methods have been developed. Using incident and emitted electrons, photons, atoms and ions, techniques have been developed to study the composition, structural, electronic and vibrational properties of surfaces. A key feature for the successful study of surface structures has been the exploitation and combination of several complementary methods.

In this chapter the basic principles, advantages and limitations of the complementary meth- ods used for this thesis will be discussed. All the presented studies included precharacterization with STM, LEED and UPS before performing the SXRD-measurements.

3.2 Scanning tunneling microscopy (STM)

Scanning tunneling microscopy (STM) was invented in 1981 by Gerd Binnig and Heinrich Rohrer [1] at IBM Z¨urich Research Laboratories, in Switzerland. The technique is based on the basic principle of the tunneling effect. A piezo-electric scanner is used to accurately position an atomically sharp tip above a sample. Changing the position in the lateral (x, y)-plane allows

–37– 38 COMPLEMENTARY METHODS

one to scan continuously across the sample surface and monitoring changes in the vertical z- position. If this distance becomes small enough (0.1 − 10) A˚ and a bias voltage is applied between the sample and the the tip, a classically forbidden potential barrier can be overcome and electrons from occupied states of the tip tunnel into unoccupied states of the sample. The tunneling current (0.1−1) nA can be observed (see Figure 3.1). The tunneling current depends exponentially on the tip–sample separation. If a feedback loop is used to adjust the vertical position to keep the current constant, the constant current scanning mode, the tip–sample separation can be kept constant with great precision, hence the topography of the surface can be measured with great accuracy. In another mode the constant height scanning mode, the z-coordinate of the tip and the bias voltage can be held constant and the variation of the tunneling current is measured, which reflects the charge density of the surface. Since the readjustment of the sample-tip distance is not needed, the scanning frequency can be higher than in the constant current scanning mode [2, 3]. In addition to scanning across the sample, information on the electronic structure at a precise location can be obtained by changing the bias voltage while measuring the tunneling current. This results in a plot of the local density of states as a function of energy within the sample, it is called Scanning Tunneling Spectroscopy (STS).

In principle, STM should only work with conducting samples and not with insulators, since the tunneling current originates from the fact that electrons from the occupied states of the tip travel through the barrier to unoccupied states of the sample. Today it is also possible to perform STM on insulators by injecting electrons into the conduction band of the insulator. The big advantage of STM is its local nature. It is suited to locally probe the surface with high resolution. The biggest limitation of STM is the inability to prepare stable, atomically- sharp tips with well-known physical and chemical properties. The unknown geometry and electronic properties of the tip are usually the largest uncertainties regarding interpretation of STM images. 3.3 LOW-ENERGY ELECTRON-DIFFRACTION (LEED) 39

Figure 3.1: Schematics of a scanning tunneling microscope. A sharp tip is moved by a piezoelectric positioning system over a sample surface. By applying a voltage between tip and sample a weak tunneling current (in the nA range) flows if the tip is sufficiently close to the sample. The positioning system is made of three orthogonal piezoelectric bars. Application of suitable voltages allows movement of the tip in x-, y- and z-directions. A feedback loop keeps the local interaction constant during the scanning of the sample.

3.3 Low-energy electron-diffraction (LEED)

Low-energy electron-diffraction (LEED) was invented in 1927 by Davisson and Germer [4, 5] and is one of the most widely used experimental probes of surface structures. The principle is similar to that of SXRD (see Chapter 2), but instead of x-ray photons impinging onto the surface, one uses electrons with low energies (50 − 300) eV. These have wavelengths compa- rable to interatomic distances, and are therefore diffracted by the periodically ordered surface structure. In contrast to SXRD, where the CTRs are recorded by rotating the sample, and keeping the photon energy constant, one changes the intersection point of the Ewald sphere with the rod varying the electron energy and hence the size of the Ewald sphere. This is called LEED I/V data analysis.

At low electron energies the mean free path of the electrons in the surface is typically 1 nm, hence LEED is a very surface sensitive technique. In principle this is a good thing for investigating surfaces, but at the same time it presents the limitations of providing no information about the system below 2 or 3 atomic layers. In addition since the interaction of these low-energy electrons with the surface atoms is high, the electrons are strongly scattered, 40 COMPLEMENTARY METHODS

and this gives rise to the problem of multiple scattering [6]. The kinematical approximation does not hold anymore in LEED I/V analysis, hence the calculations have to be performed dynamically, which is far more computationally demanding.

3.4 Ultraviolet Photoelectron Spectroscopy (UPS)

The basic physical principle behind all photoemission experiments is the photoelectric effect. When a surface of a solid is illuminated by photons of sufficiently high energy, it will emit photoelectrons. These electrons are released from either a core level, in which case the analyzing technique is called x-ray photoelectron spectroscopy (XPS), or from the valence band, then the technique is called ultraviolet photoelectron spectroscopy (UPS) [7]. The kinetic energy Ekin of the photoelectrons contains information of the binding energy EB of the respective energy level according to the following relation:

EB = hν − Ekin − φs, (3.1) where φs is the work function of the the material, the energetic difference between the Fermi level and the vacuum level. In an XPS- or UPS-experiment one plots the intensity of the detected electrons versus the energy. The discrete peaks reflect the binding energies, which are specific to each chemical element.

In the case of nanomeshes, σ-band and π-band splitting is observed, originating from the two distinct height levels of the corrugated surface combing slightly different binding energies. BIBLIOGRAPHY 41

Bibliography

[1] G. Binnig, H. Rohrer, C. Gerber, and E. Weibel: “Surface Studies by Scanning Tunneling Mi- croscopy.” Phys. Rev. Lett. 49(1), 57–61 (1982), doi:10.1103/PhysRevLett.49.57.

[2] L. E. C. van de Leemput and H. van Kempen: “Scanning Tunneling Microscopy.” Rep. Prog. Phys. 55(8), 1165–1240 (1992), doi:10.1088/0034-4885/55/8/002.

[3] G. Binnig and H. Rohrer: “In touch with atoms.” Rev. Mod. Phys. 71(2), S324–S330 (1999), doi: 10.1103/RevModPhys.71.S324.

[4] C. Davisson and L. H. Germer: “Diffraction of electrons by a crystal of nickel.” Phys. Rev. 30(6), 705–740 (1927), doi:10.1103/PhysRev.30.705.

[5] C. Davisson and L. H. Germer: “The scattering of electrons by a single crystal of nickel.” Nature 119, 558–560 (1927), doi:10.1038/119558a0.

[6] E. G. McRae: “Self-Consistent Multiple-Scattering Approach to Interpretation of Low-Energy Elec- tron Diffraction.” Surf. Sci. 8(1-2), 14 (1967), doi:10.1016/0039-6028(67)90071-4.

[7] Siegbahn: ESCA; Atomic, molecular and solid state structure studied by means of electron spec- troscopy. Nova acta regiae societatis scientiarum Upsaliensis, ser. 4, Uppsala (1967).

Chapter 4

Nanomeshes

4.1 Introduction

Nanotemplates are attracting much interest in the field of materials science research. They can be used to produce well-ordered arrays of single molecules and nanoparticles with nanometer- scale periodicity [1, 2, 3, 4]. In this context, self-organized nanotemplates are more and more the focus of investigations, due to their fairly easy fabrication. When h-BN- and graphene single layers are grown on substrates with slightly different lattice parameters, as Rh(111) or Ru(0001), they form commensurate superstructures, so-called nanomeshes [5, 6, 7]. Due to the lattice mismatch and the resulting varying strength of interaction with the substrate [8, 9, 10, 11, 12, 13] across the surface, the surfaces tend to corrugate, hence varying the height across the surface in a regular way. These sp2 hybridized layers have strong σ in-plane bonds, but also surprisingly strong π out-of-plane bonds (see Chapter 8). Depending on the substrate type these materials are grown on and their lattice mismatch to them, they might form nanomeshes, but they can also form 1 × 1 superstructures [14] or moir´e-patterns, lacking any corrugations [15].

It has been shown that nanomeshes are stable in air [16] (see Section 5) in aqueous solu- tions [1], and remain stable up to very high temperatures [17] (see Section 6). Conceptually the h-BN and graphene nanomeshes are very similar, however graphene has attracted much

–43– 44 NANOMESHES

more attention due to its unique electronic properties - it is a gapless semiconductor. For its application in making electronic devices the introduction of a bandgap is crucial. Recently it was reported that the growth on substrates can alter the electronic properties of graphene significantly; it can become metallic [18] due to a shift of the Fermi energy EF , but it can also be that a bandgap is opened and it exhibits semiconducting behaviour [19]. These findings suggest the possibility of preparing semiconducting graphene layers for future carbon-based nanoelectronic devices via direct deposition onto strongly interacting substrates.

h-BN on the other hand is purely insulating, even when grown on a substrate. Although the h-BN and graphene are similar from a structural point of view, they are very different regarding their electronic properties. The similarities of these structures and the interest- ing electronic structure of graphene, altered when grown on substrates and the potential use for nanotemplates make these materials highly interesting from a detailed structural point of view.

This chapter focuses on the properties of the nanomeshes investigated in this thesis, namely single layers of h-BN and of graphene on the surfaces of the transition metals Rh(111) and Ru(0001). A more extended overview and review about these systems can be found elsewhere [4, 20, 21, 22, 23]. First the two surfaces of Ru(0001) and Rh(111) are described, then the focus turns to the sp2 hybridized nanomesh h-BN and graphene. After a short overview of the electronic properties of these materials, a motivation for the analysis of these systems with SXRD is given.

4.2 hcp(0001)- and fcc(111)-surfaces

Ruthenium is a transition metal, with the atomic number of Z = 44. It crystallizes in the hexagonal close packed (hcp) structure. Its lattice constants are a = 2.700 A,˚ b = 2.700 A,˚ c = 4.277 A˚ [24]. Rhodium on the other hand, is a transition metal with the atomic number Z = 45, which crystallizes in a face centered cubic structure. The lattice constants of rhodium are a = 2.689 A,˚ b = 2.689 A,˚ c = 6.587 A˚ [24]. The (hcp) and the (fcc) structures both have a packing factor of 0.74, consist of closely packed planes of atoms, and have a coordination number of 12. The difference between the (hcp) and (fcc) structures is the stacking sequence. 4.2 HCP(0001)- AND FCC(111)-SURFACES 45

Figure 4.1: Schematic view of the Ru(0001)-surface. The structure starts with a layer A, on top of which one puts layer B, filling up the hcp-sites, and leaving hence the fcc-sites free. The third layer is positioned on top of the first one, hence the stacking sequence follows the ABABABA...-scheme.

Figure 4.2: Schematic view of the Rh(111)-surface. The structure starts with a closed-packed A-layer, followed by a B-layer, which fills up the (hcp)-sites. The following, third layer C, fills out the (fcc)-sites. This leads to a ABCABCABC... stacking sequence. Hence when looked from a top view, there are no holes in this structure.

The (hcp) layers cycle among the two equivalent shifted positions whereas the fcc layers cycle between three positions. As can be seen in Figure 4.1, the (hcp) structure contains only two types of planes with an alternating ABAB arrangement. Note how the atoms of the third plane are in exactly the same position as the atoms in the first plane. However, the fcc structure (see Figure 4.2) contains three types of planes with a ABCABC arrangement. Here the atoms in rows A and C are no longer aligned. 46 NANOMESHES

4.3 sp2-hybridization

In order to explain the hexagonal honeycomb structure of sp2-hybridized meshes, as h-BN and graphene, 3 orbitals in the hybrid set are required.

Let us consider graphene as an example of sp2-hybridization. In the ground-state, carbon 2 2 1 1 has a 1s 2s 2px2py electronic configuration (see Figure 4.3). The first step in the process of sp2-hybridization is that the nucleus attracts one of the electrons in the valence band, which will make one of the two 2s-electrons hop to the free 2pz orbital. This gives 4 non degenerate energy states. Because of this new electronic configuration the effective core potential has increased and the orbital structure reorganizes: The 2s orbital is mixed with two of the three available 2 2p orbitals, namely 2px,2py, forming three sp hybridized, energetically degenerate orbitals (see Figure 4.3). The name sp2 comes from the fact, that one s-orbital and two p-orbitals are involved in this process.

The unit cell of an sp2-hybridized layer is made of 2 atoms (see Figure 4.4). The correspond- ing Brillouin zone in k-space shows six equivalent K-points. If the two atoms are identical (as in free-standing graphene), the valence and conduction band are degenerate. When the sublattice symmetry is broken, (as in h-BN) the K and K’ points are no longer degenerate anymore.

4.4 Moir´epatterns

In the case of h-BN and graphene grown on substrates, it is important to know whether the structure formed is a moir´epattern or a commensurate superstructure. A moir´epattern appears when a lattice is superposed to another one with different lattice constants. The resulting structure has a much larger periodicity than either of the original patterns (see Figure 4.5). If one represents the patterns with wavevectors, ~k1 and ~k2, the periodicity of the moir´epattern is

~kmoir´e = ∆~k = ~k2 − ~k1. (4.1)

Certain structural techniques such as STM are unable to distinguish between a moir´estructure and a true corrugated nanomesh superstructure, as it is difficult to differentiate between changes 4.5 HEXAGONAL BORON NITRIDE (H-BN) ON TRANSITION METAL SURFACES 47

2 Figure 4.3: The sp -hybridization in graphene. First one of the two 2s-electrons hops to the free 2pz- state. Due to a increase in the effective core potential the orbital structure reorganizes. The 2s-orbital mixes with two of the three 2p-orbitals, which leads to three sp2 energetically degenerate hybridized orbitals. in electron density and vertical shifts in atomic positions. This problem can be overcome by using diffraction techniques for the investigations, e.g., LEED or SXRD.

4.5 Hexagonal Boron Nitride (h-BN) on transition metal surfaces

In h-BN crystals (see Figure 4.6), alternating boron (B) and nitrogen (N) atoms form a 2- dimensional plane. The strong in-plane sp2-hybridized bonds between two atoms are of a covalent character. These planes are stacked on top of each other such that each boron of the next layer is on top of another boron. They are held together via weak van der Waals interactions [25]. The lattice constants are a = b = 2.504 A˚ and c = 6.660 A˚ [26].

One can deposit single h-BN layers on transition metal surfaces via chemical vapor deposition

(CVD) of borazine (HBNH)3 [20]. On some surfaces, such as Pd(111) [27], Pt(111) [28], and Ni(111) [29, 30, 31, 32], the h-BN monolayer is flat. Because of a strong reduction of the surface reactivity once the flat monolayer of BN has been deposited the growth rate of the BN subsequently becomes extremely small. This facilitates the growth of a single monolayer film [33]. The electronic properties of this layer are almost independent of the substrate [34, 35]. 48 NANOMESHES

2 Figure 4.4: (a) The real space unit cell of sp -hybridized layers with lattice vectors a1 and a2 and the two atoms A and B is shown. The sp2-hybridization couples the two sublattices A and B. (b) The corresponding Brillouin zone in k-space is shown. K and K′ are nonequivalent, when the symmetry of the sublattice is broken, as in the case of h-BN, which consists of two different atoms. For the case of free-standing graphene, where the two sublattices are indistinguishable, this leads to a gap-less semiconductor with Dirac points at the K points.

Figure 4.5: A moir´epattern arises by the superposition of two regular patterns with slightly different lattice constants. When represented by two wave vectors, ~k1 and ~k2, the difference of the two ∆~k =

~k2 −~k1 gives the much smaller wavevector than the two original patterns had, and hence a larger distance between two maxima in the pattern.

The bonding between the mentioned substrates and the h-BN-layer is very weak, the structures formed are either of type 1×1 or they are flat moir´estructures [27]. As described in Section 4.4 moir´epatterns are not necessarily nanomeshes. The SXRD signal of a moir´e pattern lacks the 4.5 HEXAGONAL BORON NITRIDE (H-BN) ON TRANSITION METAL SURFACES 49

Figure 4.6: The layer stacking in h-BN crystals. The N sits exactly on top of a N of the subsequent layer, and so does the B.

“real reconstruction peak” (see Section 4.7).

On the other hand nanomeshes, defined by their periodic corrugation, have been observed on Rh(111) and Ru(0001) surfaces [5, 17]. Nanomesh formation is driven by the fact, that boron is attracted to the metallic surface, while nitrogen is repelled. There is a slight transfer of charge from h-BN-layer to the substrate. Since the pz-state of the nitrogen is lower than the pz-state of boron (see Figure 4.7), there is a small charge transfer from the boron pz-level to the nitrogen pz-level. Since the substrate is negatively charged, the negatively charged nitrogen will be repelled, while the positively charged boron will be attracted.

Due to a strong covalent interaction of the boron with the substrate’s dz-orbitals, the bond- ing and antibonding bands split. While the bonding orbitals of both elements are below the Fermi level, the boron antibonding band contribution remains well above the Fermi level of the system whereas part of the nitrogen band contribution antibonding is below the Fermi level and is thus partially filled (see Figure 4.7). Due to the lattice mismatch this situation changes gradually with the nanomesh-substrate registry, resulting in certain regions being attracted, where the boron is on top of a substrate atom and others being repelled, where the nitrogen are on top of the substrate atom. This leads to the formation of a commensurate superstructure, which in the case of h-BN on Rh(111) consists of 13 × 13 h-BN on 12 × 12 Rh (called 13-on-12) [5, 16, 36] (see Chapter 5 and Chapter 6), while for h-BN on Ru(0001) the structure is 14 × 14 h-BN on 13 × 13 Ru (i.e., 14-on-13) (see Chapter 7).

The exact binding energies have been calculated by ab-initio calculations [12], where the 4d 50 NANOMESHES

Figure 4.7: Diagram of the density of states around the Fermi level of h-BN grown on Rh(111) [11].

Because of the strong interaction of the pz-orbital of the boron and the dz-orbital of the Rh(111) surface, the π-band split. The antibonding band contribution of the boron remains above the Fermi level, whereas the N antibonding band is below the Fermi level and thus partially filled. This makes the B being attracted and the N being repelled. When grown on a substrate with a large enough lattice mismatch, this situation changes over a large period, and the formation of a superstructure is stimulated. transition metals exhibit the strongest bonding. It is claimed that the bond strength correlates with the d-band occupancy (see Table 4.1). The more occupied the d-shell of the element is, the lower is the binding energy.

The critical point determining whether a nanomesh, or a more free floating flat layer is formed (producing a moir´epattern) is the lattice mismatch. In the following Table 4.1 the lattice mismatches are listed for h-BN for various substrates, whereby the lattice mismatch is defined by Zangwill et al. [37] as:

a −BN − a M = h s , (4.2) as where ah−BN is the in-plane lattice constant of h-BN and as is the in-plane lattice constant of the substrate surface.

4.6 Graphene on transition metal surfaces

Graphite has a crystal structure very similar to that of h-BN. Two-dimensional sheets of carbon arranged in a honeycomb network containing two atoms per unit cell, A1 and A2, stack on top of each other to form the crystal. In contrast to h-BN the stacking of the sheets follows the 4.6 GRAPHENE ON TRANSITION METAL SURFACES 51

Element Ni Rh Ru Pd Pt Electronic configuration [Ar]4s23d8 [Kr]5s14d8 [Kr]5s14d7 [Kr]4d10 [Xe]6s14f 145d9 Structure fcc fcc hcp fcc fcc Surface (111) (111) (0001) (111) (111)

as 2.489 A˚ 2.689 A˚ 2.700 A˚ 2.751 A˚ 2.772 A˚ M 0.60% -6.88% -7.26% -8.98% -9.67%

Table 4.1: Structure and in-plane lattice (in surface coordinates) constants of some transition metals [24, 38]. The lattice mismatch compared to a bulk lattice constant of h-BN = 2.504 A˚ [39] are given by the definition M by Zangwill et al. [37] .

Figure 4.8: The stacking of graphite. Graphite follows the Bernal stacking scheme: A1 and B2 atoms of the consecutive layers are on top of each other, but A2 and B1 are obviously not, the B2 is under the unoccupied center of the adjacent cell.

Bernal stacking ABAB scheme shown in Figure 4.8. It has an in-plane lattice constant of a = b = 2.462 A˚ and a c lattice constant of 6.708 A.˚

Graphene, the constituent monolayer sheet of graphite, was discovered in 2004 by Novoselov et al. [40]. Apart from the fact that graphene has two equivalent carbon atoms in one unit cell it is structurally identical to monolayer h-BN. Although the two materials are isoelectronic, their electronic properties are completely different: while h-BN is an insulator, graphene has remarkable electronic properties and is a zero-gap semiconductor [23, 41, 42, 43]. The reason for this lies in the fact that graphene has two identical atoms in the unit cell.

Interaction between the sp2 orbitals of two neighbouring carbon atoms, forms the bonding σ 52 NANOMESHES

band and the antibonding σ∗ band. π and π∗ bands are formed by the overlap of the delocalized

2pz orbitals perpendicular to the molecular plane.

Since σ bonds are very strong, the occupied σ bands, and the unoccupied σ∗ band are well separated - the σ band is well below the Fermi level and is a valence band, whereas the σ∗ is empty and is a conduction band. Each 2pz orbital has one extra electron, the π band is half filled, the π∗ band is empty.

The electronic properties are determined by the energy levels around the Fermi energy, hence the σ and σ∗ bands can be neglected, and only the π and π∗ bands are considered. When calculating the dispersion relations according to a tight binding model for the two equal atoms in the unit cell, the valence and conduction band meet at a crossing exactly at the K point of the Brillouin zone, the Dirac point, giving rise to a single state at the Fermi energy. The valence and conduction bands are degenerate at these points, graphene is a zerogap semiconductor. This results in a relativistic behaviour of graphene’s effectively massless charge carriers (the Dirac fermions), which is the origin of the intriguing physical properties of freestanding graphene [see Figure 4.9 (a)].

In the case of h-BN, where the unit cell consists of two different atoms, the calculation leads to a band gap opening. One can also break the equivalence of the two carbon atoms in graphene, by adsorbing it on a metal substrate resulting in a change of the electronic properties [18, 19, 44, 45, 46, 47, 48]. The same is true when graphene is grown on BN(0001) [49, 50], or on SiC(0001) [47, 51]. The atoms within the graphene unit cell can no longer be considered as being identical, since the dz-orbital of the substrate starts to mix with the pz-orbital of graphene and depending at which site the graphene atoms adsorb, they interact with different strengths. The interaction with the substrate opens up a bandgap. This makes these systems very interesting, since it provides an insight about the interaction of the graphene layer with the substrate and also potentially allows one to tune its physical properties. Even on strongly interacting substrates, graphene can recover its original electronic properties and behave as if it were free-standing, by oxygen intercalation between the graphene and the substrate, as has been shown for the case of Ru(0001) [52].

Investigations of graphene/Ir(111) found that the system forms a moir´epattern with a weak interaction with the substrate [15]. The band structure of free-standing graphene is 4.6 GRAPHENE ON TRANSITION METAL SURFACES 53

Figure 4.9: a) The dispersion relation of freestanding graphene. The π- and π∗-band meet at the dirac point. Here the valence and conduction bands are degenerate and graphene is a gapless semiconduc- tor. b) The dispersion relation of graphene can change when grown on a substrate. Charge transfer between substrate and graphene shifts the Fermi energy and a band gap Egap can open, caused by the strong interaction of the pz-orbital with the dz-orbital of the substrate. Graphene shows metallic or semiconducting behaviour. almost perfectly preserved [53] and it is only 0.2 eV. However, unlike free-standing graphene, where the Fermi level lies at the conical point, the Fermi level is shifted for weak interacting substrates , there is charge transfer between the graphene and the substrate, and the graphene is doped n-type or p-type [45].

In the case of graphene on Ni(111) [54], where a 1 × 1 superstructure was observed the 2pz orbitals of graphene hybridize with the 3dz orbitals of Ni. As a result some charge is shifted from the 3d band into the empty π∗ states of graphene, causing an energy shift of the π system and a band gap opening [20]. Very similar effects have been seen for graphene/Ru(0001), where a 2 eV downshifted π band [18, 44] opens a band gap of several eV.

In contrast to the graphene/Ni(111) case, here a superstructure is formed [55], although there are large areas in the superstructure where the A and B atoms reside on similar sites as in the case of graphene/Ni(111). The formation of superstructures leads to locally different electronic structures, depending on where the atoms above the Ru(0001) surface atoms are located [13], hence to a modulated electronic structure. 54 NANOMESHES

4.6.1 The Mermin-Wagner Theorem

Graphene was for a long time believed to not exist, due to structural instabilities. The question whether a 2D crystal can be stable was addressed first in 1934 by Peierls et al. [56]. It was shown that in the standard harmonic approximation, thermal fluctuations would destroy the long-range order. Mermin and Wagner [57] proved more than 30 years later, that magnetic long-range order could not exist in 2D-crystals, in the Mermin-Wagner Theorem. Later they also extended their theory to crystalline order in 2D [58]. They showed that the amplitude of long-wavelength fluctuations grow logarithmically with the size of a 2D structure, and would therefore become infinite in structures of infinite size. A sufficiently large 2D structure, in the absence of applied lateral tension, will bend and crumple to form a fluctuating 3D structure. Ripples have been observed in suspended layers of graphene, and it has been proposed that the ripples are caused by thermal fluctuations in the material [59, 60], hence the Mermin- Wagner theorem is not violated by graphene, as graphene does not appear to be strictly a 2D structure.

4.7 Nanomeshes investigated with LEED and SXRD

As pointed out in Section 4.4 often the problem arises to distinguish between a commensurate superstructure, a nanomesh, and a moir´epattern, and that it is much easier to approach the problem in reciprocal space. However, this is not the full truth. As mentioned in Section 3.3 due to the large cross-section of the electrons interacting with matter, scattering dynamic LEED theory is necessary for the determination of atomic structures. This makes computation and analysis of LEED spot-intensities much more difficult than it is for SXRD. In particular if looking at the reconstruction peaks, in LEED it is not possible to distinguish at first sight between a corrugated commensurate layer, a nanomesh, and a “free floating layer”. Here we will focus on the h-BN/Rh(111) system (see Section 5 and 6) as an example of nanomeshes, and discuss the above mentioned problem in detail on the real reconstruction peak.

Consider the one-dimensional case in the in-plane region near the first Bragg peak (h, k)= (1, 0), and at a non-zero out-of-plane component, fixed at l = 0.4. We start with the simplest 4.7 NANOMESHES INVESTIGATED WITH LEED AND SXRD 55

case, of a non-reconstructed surface [see Figure 4.10 (a)], twelve boron atoms match up with 12 rhodium atoms. The intensity produced along the h-direction will only be visible at h =1= 12/12. There are no superstructure rods, since there is no superstructure. If we now consider the moir´epattern produced by 13 boron atoms matching up with 12 rhodium atoms the diffraction pattern signal in the h-direction will include in addition to the Bragg-rod, produced by the rhodium, also a superstructure-rod showing up at h = 13/12 [see Figure 4.10 (b)]. The signal is the Bragg-rod of the boron. Importantly, for a moir´estructure, one observes no signal at h = 11/12. Note that although this is true for SXRD, which satisfies the kinematical approximation, for strongly scattered low-energy electrons (as in LEED) multiples of the Bragg- rod, also at h = 11/12, will be seen even in a moir´estructure. Hence LEED is unable to provide immediate informations on the nature of the superstructure, e.g., whether it is a true nanomesh or a flat moir´estructure, at least not without any time consuming dynamical calculation.

We now introduce a corrugation on the boron, which can have shape as long as its periodicity is the same as that of the 12 underlying rhodium atoms. One now sees all the h = 1/12 Fourier- components [see Figure 4.10 (c)]. This is caused by the fact that the unit cell is now 12 times larger than the rhodium unit cell. In particular the satellite on h = 12/12, which sits at the same location as the large signal coming from the bulk-rhodium, and on h = 14/12 will be the strongest ones. Lastly, we include a similar corrugation on the uppermost layers of the substrate which will make, arguing the same way, appearing again all h = 1/12-rods, the strongest satellites of the Bragg-rod are the next ones, hence the h = 11/12 and the h = 13/12. In summary we will have a very strong rhodium Bragg-rod at the h = 12/12-position, a strong satellite coming from the corrugation of the rhodium on the h = 11/12-position and a strong rod on the h = 13/12-position coming from the strongest satellite of the rhodium and from the boron Bragg-rod. One can say, that although the atomic form factors for B, N, and C, are not suitable for investigating these materials with photons, the special situation of having signal coming from the weakly corrugated substrate, and signal coming from the light scattering adsorbed layers on the same rods, gives us the possibility of looking at these materials using SXRD. More than that, since the substrates investigated in this thesis, rhodium and ruthenium, both are strong scattering materials, the contrast to h-BN and graphene is high, and therefore the signals are better distinguishable. 56 NANOMESHES

Figure 4.10: Schematic view of a nanomesh. The intensities in reciprocal space reflect the situation in real space. (a) When 12 boron atoms match up with 12 rhodium atoms in two flat layers, all the intensity has to be expected on the h = 12/12-position, since there is no reconstruction and both Bragg-rods from adsorbate and substrate meet at the same point in reciprocal space. (b) When 13 boron atoms match on top of 12 substrates atoms, the Bragg-rod of the boron will be shifted towards higher q-values, namely h = 13/12, since the lattice spacings between two boron atoms is 12/13. (c) If one includes in a corrugation on the boron, defining a superlattice of 12 rhodium atoms, the result is the appearance of satellite spots of the boron- Bragg-rod, the strongest ones are the h = 12/12-rod and the h = 14/12-rod. (d) Corrugating the substrate, has a similar effect as seen with the adsorbate layer. Satellites appear next to the rhodium Bragg-rod of the rhodium, here the strongest ones are the h = 11/12 and the h = 13/12.

Using this method, we established the superstructures in Chapter 6 7 8 9 to be corru- gated and commensurate. This principle can be applied exactly the same way to a 25/23- reconstruction. There the situation is slightly more complicated, since a doubling of the fre- quency of the superstructure alone, makes every even rod be forbidden. BIBLIOGRAPHY 57

Bibliography

[1] S. Berner, M. Corso, R. Widmer, O. Groening, R. Laskowski, P. Blaha, K. Schwarz, A. Gori- achko, H. Over, S. Gsell, M. Schreck, H. Sachdev, T. Greber, and J. Osterwalder: “Boron Nitride Nanomesh: Functionality from a Corrugated Monolayer.” Angew. Chem. Int. Ed. 46(27), 5115 (2007), doi:10.1002/anie.200700234.

[2] A. Goriachko, A. A. Zakharov, and H. Over: “Oxygen-etching of h-BN/Ru(0001) nanomesh on the nano- and mesoscopic scale.” J. Phys. Chem. C 112(28), 10423–10427 (2008), doi: 10.1021/jp802359u.

[3] H. Dil, J. Lobo-Checa, R. Laskowski, P. Blaha, S. Berner, J. Osterwalder, and T. Greber: “Surface trapping of atoms and molecules with dipole rings.” Science 319(5871), 1824–1826 (2008), doi: 10.1126/science.1154179.

[4] A. Goriachko and H. Over: “Modern Nanotemplates Based on Graphene and Single Layer h-BN.” Z. Phys. Chem. 223(1-2), 157–168 (2009), doi:10.1524/zpch.2009.6030.

[5] M. Corso, W. Auw¨arter, M. Muntwiler, A. Tamai, T. Greber, and J. Osterwalder: “Boron Nitride Nanomesh.” Science 303(5655), 217–220 (2004), doi:10.1126/science.1091979.

[6] S. Marchini: Scanning Tunneling Microscopy and Spectroscopy investigations of Graphene on Ru(0001) and (CO+O) on Rh(111). Ph.D. thesis, Ludwig-Maximilians-Universit¨at M¨unchen (2007). URL http://edoc.ub.uni-muenchen.de/7975

[7] S. Marchini, S. G¨unther, and J. Wintterlin: “Scanning tunneling microscopy of graphene on Ru(0001).” Phys. Rev. B 76(7), 075429 (2007), doi:10.1103/PhysRevB.76.075429.

[8] A. B. Preobrajenski, M. A. Nesterov, M. L. Ng, A. S. Vinogradov, and N. M˚artensson: “Monolayer h-BN on lattice-mismatched metal surfaces: On the formation of the nanomesh.” Chem. Phys. Lett. 446(1-3), 119–123 (2007), doi:10.1016/j.cplett.2007.08.028.

[9] A. B. Preobrajenski, A. S. Vinogradov, M. L. Ng, E. Cavar,´ R. Westerstr¨om, A. Mikkelsen, E. Lundgren, and N. M˚artensson: “Influence of chemical interaction at the lattice-mismatched h-BN/Rh(111) and h-BN/Pt(111) interfaces on the overlayer morphology.” Phys. Rev. B 75(24), 245412 (2007), doi:10.1103/PhysRevB.75.245412.

[10] R. Laskowski, P. Blaha, T. Gallauner, and K. Schwarz: “Single-Layer Model of the Hexagonal Boron Nitride Nanomesh on the Rh(111) Surface.” Phys. Rev. Lett. 98(10), 106802 (2007), doi: 10.1103/physrevlett.98.106802. 58 BIBLIOGRAPHY

[11] R. Laskowski and P. Blaha: “Unraveling the structure of the h-BN/Rh(111) nanomesh with ab initio calculations.” J. Phys. Condens. Matter 20(6), 064207 (2008), doi:10.1088/0953- 8984/20/6/064207.

[12] R. Laskowski, P. Blaha, and K. Schwarz: “Bonding of hexagonal BN to transition metal sur- faces: An ab initio density-functional theory study.” Phys. Rev. B 78(4), 045409 (2008), doi: 10.1103/PhysRevB.78.045409.

[13] B. Wang, M. L. Bocquet, S. Marchini, S. G¨unther, and J. Wintterlin: “Chemical origin of a graphene moir´eoverlayer on Ru(0001).” Phys. Chem. Chem. Phys. 10(24), 3530–3534 (2008), doi: 10.1039/b801785a.

[14] W. Auw¨arter, H. Suter, H. Sachdev, and T. Greber: “Synthesis of One Monolayer of Hexagonal

Boron Nitride on Ni(111) from B-Trichloroborazine (ClBNH)3.” Chem. Mater. 16(2), 343 (2004), doi:10.1021/cm034805s.

[15] A. T. N’Diaye, J. Coraux, T. N. Plasa, C. Busse, and T. Michely: “Structure of epitaxial graphene on Ir(111).” New J. Phys. 10, 043033 (2008), doi:10.1088/1367-2630/10/4/043033.

[16] O. Bunk, M. Corso, D. Martoccia, R. Herger, P. R. Willmott, B. D. Patterson, J. Osterwalder, J. F. van der Veen, and T. Greber: “Surface X-ray diffraction study of boron-nitride nanomesh in air.” Surf. Sci. 601(2), L7–L10 (2007), doi:10.1016/J.Susc.2006.11.018.

[17] A. Goriachko, Y. He, M. Knapp, and H. Over: “Self-Assembly of a Hexagonal Boron Nitride Nanomesh on Ru(0001).” Langmuir 23(6), 2928–2928 (2007), doi:10.1021/la062990t.

[18] T. Brugger, S. G¨unther, B. Wang, J. H. Dil, M.-L. Bocquet, J. Osterwalder, J. Wintterlin, and T. Greber: “Comparison of electronic structure and template function of single-layer graphene and a hexagonal boron nitride nanomesh on Ru(0001).” Phys. Rev. B 79(4), 045407 (2009), doi: 10.1103/PhysRevB.79.045407.

[19] S.-Y. Kwon, C. V. Cobanu, V. Petrova, V. B. Shenoy, J. Bare˜no, V. Gambin, I. Petrov, and S. Kodambaka: “Growth of Semiconducting Graphene on Palladium.” Nano Lett. (accepted) (2009), doi:10.1021/nl902140j.

[20] C. Oshima and A. Nagashima: “Ultra-thin epitaxial films of graphite and hexagonal boron nitride on solid surfaces.” J. Phys. Condens. Matter 9(1), 1–20 (1997), doi:10.1088/0953-8984/9/1/004.

[21] T. Greber: “Graphene and Boron Nitride Single Layers.” Preprint at http://arxiv:0904.1520v1 (2009). BIBLIOGRAPHY 59

[22] J. Wintterlin and M. L. Bocquet: “Graphene on metal surfaces.” Surf. Sci. 603(10-12), 1841–1852 (2009), doi:10.1016/j.susc.2008.08.037.

[23] A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim: “The electronic properties of graphene.” Rev. Mod. Phys. 81(1), 109–162 (2009), doi:10.1103/RevModPhys.81.109.

[24] N. W. Ashcroft and N. D. Mermin: Solid State Physics. Holt, Rinehart and Winston, New York (1969).

[25] N. Ooi, A. Rairkar, L. Lindsley, and J. Adams: “Electronic structure and bonding in hexagonal boron nitride.” J. Phys. Condens. Matter 18(1), 97 (2006), doi:10.1088/0953-8984/18/1/007.

[26] V. L. Solozhenko, G. Will, and F. Elf: “Isothermal Compression of Hexagonal Graphite-Like Boron- Nitride up to 12 Gpa.” Solid State Commun. 96(1), 1–3 (1995), doi:10.1016/0038-1098(95)00381-9.

[27] M. Morscher, M. Corso, T. Greber, and J. Osterwalder: “Formation of single layer h-BN on Pd(111).” Surf. Sci. 600(16), 3280 (2006), doi:10.1016/j.susc.2006.06.016.

[28] E. Cavar,´ R. Westerstr¨om, A. Mikkelsen, E. Lundgren, A. S. Vinogradov, M. L. Ng, A. B. Preobra- jenski, A. A. Zakharov, and N. M˚artensson: “A single h-BN layer on Pt(111).” Surf. Sci. 602(9), 1722–1726 (2008), doi:10.1016/J.Susc.2008.03.008.

[29] Y. Gamou, M. Terai, A. Nagashima, and C. Oshima: “Atomic structural analysis of a monolayer epitaxial film of hexagonal boron nitride Ni(111) studied by LEED intensity analysis.” Sci. Rep. RITU 44(2), 211–214 (1997).

[30] W. Auw¨arter, T. J. Kreutz, T. Greber, and J. Osterwalder: “XPD and STM investigation of hexagonal boron nitride on Ni(111).” Surf. Sci. 429(1-3), 229–236 (1999), doi:10.1016/s0039- 6028(99)00381-7.

[31] G. B. Grad, P. Blaha, K. Schwarz, W. Auw¨arter, and T. Greber: “Density functional theory investigation of the geometric and spintronic structure of h-BN/Ni(111) in view of photoemission and STM experiments.” Phys. Rev. B 68(8), 085404 (2003), doi:10.1103/physrevb.68.085404.

[32] M. N. Huda and L. Kleinman: “h-BN monolayer adsorption on the Ni(111) surface: A density functional study.” Phys. Rev. B 74(7), 075418 (2006), doi:10.1103/physrevb.74.075418.

[33] A. B. Preobrajenski, A. S. Vinogradov, and N. M˚artensson: “Ni 3dBN π hybridization at the h- BNNi(111) interface observed with core-level spectroscopies.” Phys. Rev. B 70(16), 165404 (2004), doi:10.1103/physrevb.70.165404.

[34] A. Nagashima, N. Tejima, Y. Gamou, T. Kawai, and C. Oshima: “Electronic Structure of Mono- 60 BIBLIOGRAPHY

layer Hexagonal Boron Nitride Physisorbed on Metal Surfaces.” Phys. Rev. Lett. 75(21), 3918 (1995), doi:10.1103/physrevlett.75.3918.

[35] A. Nagashima, N. Tejima, Y. Gamou, T. Kawai, and C. Oshima: “Electronic dispersion relations of monolayer hexagonal boron nitride formed on the Ni(111) surface.” Phys. Rev. B 51(7), 4606 (1995), doi:10.1103/physrevb.51.4606.

[36] D. Martoccia, S. A. Pauli, T. Brugger, T. Greber, B. D. Patterson, and P. R. Willmott: “h−BN on Rh(111): Persistence of a commensurate 13-on-12 superstructure up to high temperatures.” Surf. Sci. 604(5-6), L9–L11 (2010), doi:10.1016/J.Susc.2009.12.016.

[37] A. Zangwill: Physics at surfaces. Cambridge University Press, Cambridge (1988).

[38] Entry [5 - 685] of database Powder Diffraction File PDF 2, Release 2001, International Centre for Diffraction Data (ICDD), Newton Square, Pennsylvania, USA.

[39] E. K. Sichel, R. E. Miller, M. S. Abrahams, and C. J. Buiocchi: “Heat-Capacity and Thermal- Conductivity of Hexagonal Pyrolytic Boron-Nitride.” Phys. Rev. B 13(10), 4607–4611 (1976), doi: 10.1103/PhysRevB.13.4607.

[40] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov: “Electric field effect in atomically thin carbon films.” Science 306(5296), 666–669 (2004), doi:10.1126/science.1102896.

[41] K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim: “Two-dimensional atomic crystals.” PNAS 102(30), 10451–10453 (2005), doi: 10.1126/science.1102896.

[42] C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer: “Electronic confinement and coherence in patterned epitaxial graphene.” Science 312(5777), 1191–1196 (2006), doi: 10.1126/science.1125925.

[43] H. B. Heersche, P. Jarillo-Herrero, J. B. Oostinga, L. M. K. Vandersypen, and A. F. Morpurgo: “Bipolar supercurrent in graphene.” Nature 446(7131), 56–59 (2007), doi:10.1038/Nature05555.

[44] F. J. Himpsel, K. Christmann, P. Heimann, D. E. Eastman, and P. J. Feibelman: “Adsorbate Band Dispersions for C on Ru(0001).” Surf. Sci. 115(3), L159–L164 (1982), doi:10.1016/0039- 6028(82)90379-X.

[45] P. A. Khomyakov, G. Giovannetti, P. C. Rusu, G. Brocks, J. van den Brink, and P. J. Kelly: BIBLIOGRAPHY 61

“First-principles study of the interaction and charge transfer between graphene and metals.” Phys. Rev. B 79(19), 195425 (2009), doi:10.1103/Physrevb.79.195425.

[46] E. Sutter, D. P. Acharya, J. T. Sadowski, and P. Sutter: “Scanning tunneling microscopy on epitaxial bilayer graphene on ruthenium (0001).” Appl. Phys. Lett. 94(13), 133101 (2009), doi: 10.1063/1.3106057.

[47] X. Y. Peng and R. Ahuja: “Symmetry Breaking Induced Bandgap in Epitaxial Graphene Layers on SiC.” Nano Lett. 8(12), 4464–4468 (2008), doi:10.1021/Nl802409q.

[48] D. Eom, D. Prezzi, K. T. Rim, H. Zhou, M. Lefenfeld, S. Xiao, C. Nuckolls, M. S. Hybertsen, T. F. Heinz, and G. W. Flynn: “Structure and Electronic Properties of Graphene Nanoislands on Co(0001).” Nano Lett. 9(8), 2844–2848 (2009), doi:10.1021/Nl900927f.

[49] T. Kawasaki, T. Ichimura, H. Kishimoto, A. A. Akbar, T. Ogawa, and C. Oshima: “Dou- ble atomic layers of graphene/monolayer h-BN on Ni(111) studied by scanning tunneling mi- croscopy and scanning tunneling spectroscopy.” Surf. Rev. Lett. 9(3-4), 1459–1464 (2002), doi: 10.1142/S0218625X02003883.

[50] G. Giovannetti, P. A. Khomyakov, G. Brocks, P. J. Kelly, and J. van den Brink: “Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations.” Phys. Rev. B 76(7), 073103–1 (2007), doi:10.1103/PhysRevB.76.073103.

[51] S. Y. Zhou, G. H. Gweon, A. V. Fedorov, P. N. First, W. A. De Heer, D. H. Lee, F. Guinea, A. H. C. Neto, and A. Lanzara: “Substrate-induced bandgap opening in epitaxial graphene.” Nat. Mater. 6(10), 770–775 (2007), doi:10.1038/nmat2003.

[52] H. Zhang, Q. Fu, Y. Cui, D. L. Tan, and X. H. Bao: “Growth Mechanism of Graphene on Ru(0001)

and O2 Adsorption on the Graphene/Ru(0001) Surface.” J. Phys. Chem. C 113(19), 8296–8301 (2009), doi:10.1021/Jp810514u.

[53] I. Pletikosi´c, M. Kralj, P. Pervan, R. Brako, J. Coraux, A. T. N’Diaye, C. Busse, and T. Michely: “Dirac Cones and Minigaps for Graphene on Ir(111).” Phys. Rev. Lett. 102(5), 056808 (2009), doi:10.1103/PhysRevLett.102.056808.

[54] G. Bertoni, L. Calmels, A. Altibelli, and V. Scrin: “First-principles calculation of the electronic structure and EELS spectra at the graphene/Ni(111) interface.” Phys. Rev. B 71(7) (2005), doi: 10.1103/PhysRevB.71.075402.

[55] D. Martoccia, P. R. Willmott, T. Brugger, M. Bj¨orck, S. G¨unther, C. M. Schlep¨utz, A. Cervel- lino, S. A. Pauli, B. D. Patterson, S. Marchini, J. Wintterlin, W. Moritz, and T. Greber: 62 BIBLIOGRAPHY

“Graphene on Ru(0001): A 25×25 Supercell.” Phys. Rev. Lett. 101(12), 126102 (2008), doi: 10.1103/PhysRevLett.101.126102.

[56] R. Peierls: “The vacuum in Dirac’s theory of the positive electron.” Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences 146(A857), 0420–0441 (1934), doi:10.1098/rspa.1934.0164.

[57] N. D. Mermin and H. Wagner: “Absence of Ferromagnetism or Antiferromagnetism in One- or 2-Dimensional Isotropic Heisenberg Models.” Phys. Rev. Lett. 17(22), 1133 (1966), doi: 10.1103/PhysRevLett.17.1133.

[58] N. D. Mermin: “Crystalline Order in 2 Dimensions.” Phys. Rev. 176(1), 250 (1968), doi: 10.1103/PhysRev.176.250.

[59] A. Fasolino, J. H. Los, and M. I. Katsnelson: “Intrinsic ripples in graphene.” Nat. Mater. 6(11), 858–861 (2007), doi:10.1038/nmat2011.

[60] J. M. Carlsson: “Buckle or break.” Nat. Mater. 6(11), 801–802 (2007), doi:10.1038/nmat2051. Chapter 5

Surface X-ray diffraction study of boron-nitride nanomesh in air

The work presented in this chapter has been published in:

O. Bunk, M. Corso, D. Martoccia, R. Herger, P.R. Willmott, B.D. Patterson, J. Osterwalder, J.F. van der Veen, T. Greber: “Surface X-ray diffraction study of boron-nitride nanomesh in air.” Surf. Sci. 601(2), L7-L10 (2007), doi:10.1016/J.Susc.2006.11.018 a

artikel1.pdf is the online version of the library Zentralbibliothek Z¨urich

Abstract

The hexagonal boron-nitride nanomesh surface reconstruction on Rh(1 1 1) [Corso et al., Science 303 (2004) 217-220] has been investigated using surface x-ray diffrac- tion utilizing synchrotron radiation. This unique structure has been found to be stable under ambient atmosphere which provides an important basis for technolog- ical applications like templating and coating. The previously suggested (12 × 12) periodicity of this reconstruction has been unambiguously confirmed and structural

–63– 64 SURFACE X-RAY DIFFRACTION STUDY OF BORON-NITRIDE NANOMESH IN AIR

features are discussed in the light of the x-ray diffraction results.

Reprinted with kind permission from Elsevier. a Note that you need a subscription for this journal to directly access the article. Surface Science 601 (2007) L7–L10 www.elsevier.com/locate/susc Surface Science Letters Surface X-ray diffraction study of boron-nitride nanomesh in air

O. Bunk a,*, M. Corso b, D. Martoccia a, R. Herger a, P.R. Willmott a, B.D. Patterson a, J. Osterwalder b, J.F. van der Veen a,c, T. Greber b

a Research Department Synchrotron Radiation and Nanotechnology, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland b Physik-Institut, Universita¨tZu¨rich, 8057 Zu¨rich, Switzerland c ETH Zurich, 8093 Zu¨rich, Switzerland

Received 3 October 2006; accepted for publication 13 November 2006 Available online 4 December 2006

Abstract

The hexagonal boron-nitride ‘nanomesh’ surface reconstruction on Rh(111) [Corso et al., Science 303 (2004) 217–220] has been inves- tigated using surface X-ray diffraction utilizing synchrotron radiation. This unique structure has been found to be stable under ambient atmosphere which provides an important basis for technological applications like templating and coating. The previously suggested (12 · 12) periodicity of this reconstruction has been unambiguously confirmed and structural features are discussed in the light of the X-ray diffraction results. Ó 2006 Elsevier B.V. All rights reserved.

Keywords: Surface X-ray diffraction; Boron-nitride; Rhodium; Nanomesh

1. Introduction view is it important to disentangle the delicate balance in the surface free energy between h-BN and substrate contri- At elevated temperatures borazine decomposes on butions and the processes that lead to the formation of this Rh(111) to form a self assembled surface reconstruction fascinating structure and related structures on other sub- of thermally very stable hexagonal boron-nitride (h-BN) strates. For applications, it is mandatory to have detailed [1]. The unit cell of this highly regular structure is, at knowledge of the atomic and electronic structure of the 32 A˚ , huge by surface science standards. The detailed surface for utilizing it as an oxygen- and carbon-free geometry of this ‘nanomesh’ is still under debate but major template, e.g., for the production of nanocatalysts and efforts are being taken to further investigate and utilize this nanomagnets. unique system. This is attested, for example, by the forma- To solve the structure of a reconstruction involving sev- tion of a specific targeted research project ‘NanoMesh’ eral hundred atoms the best technique currently applicable supported within the sixth framework program (FP6) of is surface X-ray diffraction (SXRD) [6–8]. X-rays easily the European Commission, a recent NanoMesh workshop, penetrate the surface and are therefore sensitive to the and the successful use of the nanomesh as template for the structure of an extended surface region rather than only ordering of fullerenes [1]. the topmost layer. The data can be analyzed within the Related but different structures of hexagonal boron- kinematical framework and this facilitates solving such nitride have been reported for other surfaces like for exam- large reconstructions. However, due to the low scattering ple Ru(0001), Pt(111) [2,3], Cu(111), Ni(111) [4] and cross-sections of boron and nitrogen, is it necessary to per- Pd(110) [5]. From a fundamental and an applied point of form such an experiment at a 3rd-generation synchrotron source. * Corresponding author. Tel.: +41 563103077. With applications like templating and ordering of E-mail address: [email protected] (O. Bunk). liquids in mind, we studied the nanomesh structure on

0039-6028/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2006.11.018 LETTERS SURFACE SCIENCE L8 O. Bunk et al. / Surface Science 601 (2007) L7–L10

Fig. 1. Constant current STM images measured at It = 1 nA and Vs = À1 V. (a) STM image of the h-BN on Rh(111) nanomesh taken after preparation in UHV. The nanomesh survived 60 h air exposure as demonstrated by (b) STM and LEED images. (c) A short annealing up to 950 K is enough to remove a

relevant part of the contaminants (as H2O, O2,CO2, and CO) from the surface and bring the nanomesh back to its initial (pre-air exposure) configuration.

Rh(111) under ambient conditions. It turned out that the c = 1/3[111]cubic. The cubic coordinates are in units of nanomesh is stable even under these extreme conditions, the rhodium lattice constant, 3.80 A˚ at 300 K. in contrast to typical surface reconstructions, which nor- mally require ultra-high vacuum to be preserved. 3. Results and discussion

2. Experimental One of the main results of our investigations is the sta- bility of the nanomesh reconstruction under ambient atmo- The samples were prepared in an ultra-high vacuum sphere. As an example, the effect of a 60 h exposure to air is (UHV) system equipped with low energy electron diffrac- shown in Fig. 1. The basic structural elements can still be tion and a scanning tunneling microscope (STM) [9]. The recognized after this prolonged exposure. After removing Rh(111) surface has been cleaned by repeated sputtering the adsorbates by a short annealing at 950 K, the original and annealing cycles. The surface was held at 1070 K and structure is restored. This means that this unique surface exposed to borazine at a pressure of 3 · 10À7 mbar, then reconstruction is an ideal candidate for practical applica- subsequently cooled down to room temperature. tions, such as its use as a template for the production of As a pre-study of the stability of the reconstruction nanomaterials. STM investigations have been performed before and after That the nanomesh structure is a commensurate recon- a 60 h air exposure, see Fig. 1. struction with a (12 · 12) unit cell has been confirmed by Freshly prepared samples for the X-ray experiments in-plane scans along directions of high symmetry. An were transferred to the beamline and mounted under ambi- example is shown in Fig. 2. The (13/12 0) peak of the ent conditions inside a chamber with Kapton windows. reconstruction is of course weak but clearly observable The chamber was flushed by a constant overpressure of and exactly at the expected position. helium to reduce the background scattering. The X-ray photon energy was set to 15.0 keV and the glancing angle of incidence to 0.20°. A dataset consisting of 816 fractional order and 17 integer order in-plane reflections was re- corded. Details about the beamline, the surface diffracto- meter and the data acquisition using a novel 2D pixel detector can be found elsewhere [10,11]. The integrated intensity of the recorded reflections was determined and the standard geometrical correction factors applied [11]. Averaging reflections which are equivalent due to the p3m symmetry of the substrate yielded 402 fractional and nine integer order reflections. The systematic error determined in this standard averaging procedure [7] was as high as 74%, rendering a quantitative data analysis impossible. Among other things is the use of the stationary geometry without sample rocking scans [12] and scattering from the sample holder responsible for this. Nevertheless, valuable qualitative structural information can be obtained Fig. 2. SXRD intensity profile recorded in the plane of the surface (l = 0.07) at constant, k = 0. The (1 0 0.07) peak of the Rh(111) substrate from the SXRD data. and the (13/12 0 0.07) peak of the nanomesh reconstruction are observed, In the following we use the conventional surface coordi- ·   thereby confirming a commensurate superstructure with a (12 12) nate system with a ¼ 1=2½101Šcubic; b ¼ 1=2½110Šcubic, and Rh(111) unit cell. SURFACE SCIENCE

LETTERS

O. Bunk et al. / Surface Science 601 (2007) L7–L10 L9

Fig. 3. Patterson functions of h-BN on Rh(111). Each peak of these contour plots of the Patterson function calculated from the in-plane reflections corresponds to an important interatomic distance projected in the surface plane. (a) The Patterson function calculated from all and (b) only from the fractional order reflections is shown. The observed distances show a clear fingerprint of a (13 · 13) coincidence lattice of h-BN on a (12 · 12) Rh(111) unit cell.

The Patterson function is the auto correlation function A regular mesh of 12 · 12 peaks over the (12 · 12) unit cell of the electron density. The peaks in the Patterson function is observed.2 correspond to interatomic distances. The projection of this The Patterson function calculated from the fractional function in the surface plane can be calculated from the order reflections alone is only sensitive to the reconstructed near in-plane reflections which have a small momentum surface region, i.e., to the h-BN nanomesh and any Rh transfer perpendicular to the surface [6–8]. A contour plot atoms showing in-plane deviations from their bulk posi- of this projection is shown in Fig. 3. Taking both integer tions, see Fig. 3b. Again a hexagonal structure can be ob- and fractional order reflections into account, the Patterson served but this time with 13 · 13 peaks within the (12 · 12) function is sensitive to both the bulk-like substrate and the unit cell. This is a clear fingerprint of the nanomesh, which reconstructed surface region. The resulting contour plot is has been interpreted as a coincidence structure of 13 h-BN shown in Fig. 3a. The plot is dominated by peaks originat- per 12 Rh units [1]. The internal structure of the nanomesh ing from interatomic distances between bulk Rh atoms cannot be deduced from the Patterson function. However, since these atoms scatter significantly more than h-BN.1 one more important point can be made: The Rh substrate

1 Rh has Z = 45 electrons compared to Z = 5 for B and Z = 7 for N, 2 The shift vector from one to the following bulk Rh layer is (1/32/3À1) i.e., Rh scatters about 452/52 = 81 times stronger than B and 41 times and the Patterson function is sensitive to the projection of all these layers stronger than N. in the surface plane. LETTERS SURFACE SCIENCE L10 O. Bunk et al. / Surface Science 601 (2007) L7–L10

does not exhibit significant relaxations since otherwise the Dominik Meister, Michael Lange and Martin Klo¨ckner Patterson function calculated from the fractional order for technical support. reflections, Fig. 3b, would be dominated by the Rh signal in the vicinity of points corrsponding to bulk distances, References i.e., peak positions in Fig. 3a. Therefore we can conclude that the adsorbate–substrate interaction is sufficiently [1] M. Corso, W. Auwa¨rter, M. Muntwiler, A. Tamai, T. Greber, J. strong to yield a commensurate and long-range well- Osterwalder, Science 303 (2004) 217. [2] M.T. Paffett, R.J. Simonson, P. Papin, R.T. Paine, Surf. Sci. 232 ordered structure but does not induce strong relaxations (1990) 286. of the Rh atoms from their bulk-like positions in the sur- [3] F. Mu¨ller, K. Sto¨we, H. Sachdev, Chem. Mater. 17 (2005) 3464. face plane. [4] A.B. Preobrajenski, A.S. Vinogradov, N. Ma˚rtensson, Surf. Sci. 582 (2005) 21. 4. Summary and outlook [5] M. Corso, T. Greber, J. Osterwalder, Surf. Sci. 577 (2005) L78. [6] R. Feidenhans’l, Surf. Sci. Rep. 10 (1989) 105. [7] I.K. Robinson, Surface crystallography, in: G.S. Brown, D.E. We have investigated the nanomesh structure of hexag- Moncton (Eds.), Handbook on Synchrotron Radiation, vol. 3, onal boron-nitride on Rh(111). This unique surface recon- North-Holland, Amsterdam, 1991, p. 221 (Chapter 7). struction has been found to be stable under prolonged [8] H. Dosch, Critical Phenomena at Surfaces and Interfaces – Evanes- exposure to ambient atmosphere and X-ray radiation. cent X-ray and Neutron Scattering, Springer, New York, 1992. · [9] W. Auwa¨rter, T.J. Kreutz, T. Greber, J. Osterwalder, Surf. Sci. 429 The initially proposed (12 12) unit cell has been (1999) 229. confirmed by the SXRD results. As a preliminary result [10] B.D. Patterson, R. Abela, H. Auderset, Q. Chen, F. Fauth, F. Gozzo, indications have been presented that the nanomesh is a G. Ingold, H. Ku¨hne, M. Lange, D. Maden, D. Meister, P. Pattison, coincidence structure of 13 h-BN units per 12 Rh substrate T. Schmidt, B. Schmitt, C. Schulze-Briese, M. Shi, M. Stampanoni, units and that no major deviations from the in-plane bulk P.R. Willmott, Nucl. Instr. Meth. Phys. Res. A 540 (2005) 42. [11] C.M. Schlepu¨tz, R. Herger, P.R. Willmott, B.D. Patterson, O. Bunk, positions occur for the bulk Rh atoms. C. Bro¨nnimann, B. Henrich, G. Hu¨lsen, E.F. Eikenberry, Acta Cryst. A detailed three-dimensional structure determination of A 61 (2005) 418. the nanomesh structure in UHV is planned to gain a de- [12] E. Vlieg, J. Appl. Cryst. 30 (1997) 532. tailed picture of the structure including all atomic positions.

Acknowledgements

This work was performed at the Swiss Light Source, Paul Scherrer Institut, Villigen, Switzerland. We thank Chapter 6 h-BN on Rh(111): Persistence of a commensurate 13-on-12 superstructure up to high temperatures

The work presented in this chapter has been published in:

D. Martoccia, S.A. Pauli, T. Brugger, T. Greber, B.D. Patterson, P.R. Willmott: “h-BN on Rh(111): Persistence of a commensurate 13-on-12 superstructure up to high temperatures.” Surf. Sci. 604(5-6), L9-L11 (2010), doi:10.1016/J.Susc.2009.12.016 a

artikel2.pdf is the online version of the library Zentralbibliothek Z¨urich

Abstract

We present a high-resolution surface x-ray diffraction study of hexagonal boron ni- tride (h-BN) on the surface of Rh(111). The previously observed commensurate 13-on-12 superstructure for this system is stable in the temperature range between room temperature and 830o C. Surface x-ray diffraction measurements up to 830o C

–69– 70 H-BN ON RH(111): PERSISTENCE OF A 13-ON-12 SUPERSTRUCTURE

on the superstructure show no sign of a shift towards a different superstructure, demonstrating the high thermal stability and strong bonding between film and substrate. At lower temperatures, an anomalous thermal expansion behaviour of the topmost surface region of rhodium is observed, where the rhodium in-plane lattice constant remains invariant. This can be explained by the h-BN single-layer being compressively strained, whereby the strong bonding to the substrate causes the latter to be tensile strained.

Reprinted with kind permission from Elsevier. a Note that you need a subscription for this journal to directly access the article. Surface Science 604 (2010) L9–L11

Contents lists available at ScienceDirect

Surface Science

journal homepage: www.elsevier.com/locate/susc

Surface Science Letters h-BN on Rh(111): Persistence of a commensurate 13-on-12 superstructure up to high temperatures

D. Martoccia a, S.A. Pauli a, T. Brugger b, T. Greber b, B.D. Patterson a, P.R. Willmott a,* a Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen, Switzerland b Institute of Physics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland article info abstract

Article history: We present a high-resolution surface X-ray diffraction study of hexagonal boron nitride (h-BN) on the Received 4 November 2009 surface of Rh(111). The previously observed commensurate 13-on-12 superstructure for this system is Accepted for publication 16 December 2009 stable in the temperature range between room temperature and 830 °C. Surface X-ray diffraction mea- Available online 29 December 2009 surements up to 830 °C on the superstructure show no sign of a shift towards a different superstructure, demonstrating the high thermal stability and strong bonding between film and substrate. At lower tem- Keywords: peratures, an anomalous thermal expansion behaviour of the topmost surface region of rhodium is Boron nitride observed, where the rhodium in-plane lattice constant remains invariant. This can be explained by the Rh(111) (h-BN) single-layer being compressively strained, whereby the strong bonding to the substrate causes Surface X-ray diffraction Superstructure the latter to be tensile strained. Nanomesh Ó 2009 Elsevier B.V. All rights reserved. Low-energy electron-diffraction Ultraviolet photoelectron spectroscopy Scanning tunneling microscopy

1. Introduction X-ray diffraction (SXRD) experiments confirmed a large unit cell for the (h-BN) layer, consisting of (13 13) N and (13 13) B   The technological goal of engineering template structures on atoms above a substrate-surface unit cell of (12 12) Rh atoms  the scale of a few nanometers for the purpose of creating regular [10] (referred henceforth as 13-on-12). The periodicity of the two-dimensional arrays of molecules has important potential superstructure is 3.22 nm. Recently it was reported in a LEED study applications, e.g., in molecular recognition [1]. This task can be ad- that (h-BN) grown on Rh–YSZ–Si(111), a system better suited for dressed by the formation of superstructures, which can act as technological applications, exhibits a (14 14) (h-BN) on  nanotemplates. The size and stability in different physical environ- (13 13) Rh(111) superstructure [11]. It was argued that the dif-  ments of the superstructure cell is of fundamental importance. In ferent thermal expansion behaviours of the multilayer substrates 2004, a highly regular mesh was found to form when a clean and the single crystal substrate is the reason for the formation of

Rh(111) surface was exposed to borazine, (HBNH)3, at high tem- the different sized superstructures. Similar structures were also perature [2]. This so-called hexagonal boron nitride (h-BN) nano- found for (h-BN)/Ru(0001) [3,12,13] and for graphene/Ru(0001) mesh has been shown to act as an ideal template for assembling [14–17]. nanoparticles [3] or trapping single molecules [4,1,5]. The (h-BN)/Rh structure results as a consequence of a balance From low-energy electron-diffraction (LEED) measurements [2] between repulsive forces acting on N and attractive forces acting (which show a surface reconstruction), ultraviolet photoelectron on the B atoms. The strength of these forces varies with the lateral spectroscopy (UPS) measurements (which reveal a r-band split- BN position relative to the underlying Rh-substrate atoms – the ting [2]); scanning tunneling microscopy (STM) [3,4,6], and subse- (h-BN) monolayer therefore deforms (corrugates) vertically [7,8]. quently from density functional theory calculations [7–9], the This theoretically predicted, highly corrugated monolayer struc- structural model of the nanomesh has been deduced to be a single ture was later confirmed experimentally by STM [4]. Although corrugated BN layer consisting of hexagonally arranged ‘‘high” and there are several reports on the growth of this system, the explana- ‘‘low” regions formed by differences in the chemical bonding tions why the reconstruction adopts a 13-on-12 signature are rare strength of the B and N atoms to the Rh atoms underneath. Surface [11]. To precisely assess the effect of the commensurate fit of the

* Corresponding author. (h-BN) with respect to the substrate we performed high-resolution E-mail address: [email protected] (P.R. Willmott). surface X-ray diffraction (SXRD) measurements. We measured the

0039-6028/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2009.12.016 LETTERS SURFACE SCIENCE L10 D. Martoccia et al. / Surface Science 604 (2010) L9–L11

dependence of the superstructure lattice constant on the tempera- peak – since SXRD is not affected by multiple scattering (it satisfies ture and compared it to expectations from the known thermal to a high degree of accuracy the kinematical approximation), this expansion coefficients of bulk Rh and (h-BN). peak can only arise if the system exhibits a true commensurate superstructure, which in this case is due to a corrugation over 2. Experimental 12 12 Rh-atoms. Such a signal would not be observed in a simple  Moiré structure resulting from the coincidental overlay of a flat (h- The single-crystal Rh(111) surface was prepared in an ultra- BN) monolayer on a flat Rh-substrate. This peak is still observed at high vacuum (UHV) system equipped with LEED, STM and UPS 780 °C, a sign that even at these high temperatures, the commen- by the standard preparation method [2,12]. The growth tempera- surate superstructure remains well defined. ture was 750 °C. UPS and LEED measurements after preparation The temperature-dependent in-plane lattice constant of bulk and directly before transfer under UHV to the Materials Science rhodium, aRh [18], and bulk (h-BN) [19] given in Angstrom are: beamline, Swiss Light Source, Paul Scherrer Institut, confirmed ffiffiffi 6 9 2 the presence of the (h-BN) nanomesh. aRh 3:8026=p2 29:27 10À T 10:49 10À T ¼ þ  Á þ  Á 12 3 The nanomesh was investigated by SXRD using a beam energy 0:54 10À T 1 þ  Á ð Þ of 12.398 keV (1.00 Å) by recording six peaks [given in reciprocal 6 9 ah BN 2:504 7:42 10À T 25 4:79 10À T 25 ; 2 lattice units (r.l.u.) of the rhodium bulk] per temperature value, À ¼ À  Áð À Þþ  ð À Þ ð Þ at the h = 11/12, h =1, h = 13/12 and h = 11/12, h = 1 and À À ° h = 13/12 positions, whereby k = 0 and l = 1.2 remained constant. with the temperature T given in C. However, in this system com- À The angle of the incoming X-rays was fixed to the critical angle, prising of only a single monolayer of (h-BN) it is possible that the in-plane lattice constant may deviates significantly in its tempera- a 0:315 for Rh at this X-ray energy, where the X-ray evanes- crit ¼ cent wave intensity is strongest, and only penetrates the surface to ture dependence from that of bulk (h-BN). There is no literature a depth of a few nanometers. At each peak position a high-resolu- on the lattice constant of free-floating (h-BN) monolayers, so we as- tion scan covering at least a range of ±0.04 r.l.u. was performed. sume here that it follows a similar temperature dependence to the The background was fit with a polynomial function and was sub- bulk lattice constant. tracted from the measured data. The resulting signal itself was fit The measured in-plane Rh-lattice constant at room temperature using a pseudo-Voigt function. At each new temperature, enough is 2.689 Å, in agreement with the literature [18]. However, we time was allowed to ensure thermal equilibration (which was should view this value with some caution. The controlling diffrac- especially important at lower temperatures) before the sample tometer software (SPEC) fits the lattice parameters a, b, c, a, b, and was carefully realigned and crystallographically oriented. The inte- c. After careful analysis of these values as a function of tempera- ger Bragg-rod positions of the Rh-substrate were used to deter- ture, we estimate that the systematic errors for the lattice con- mine the substrate lattice constant. Previous temperature stants are ±0.01 Å. The statistical errors are at least an order of calibrations of the substrate heater ensured the accuracy of the magnitude smaller. temperature to better than ±20 °C. In Fig. 2a we compare the expected lattice expansion (blue solid line) [see Eq. (1)] for the bulk rhodium with the measured lattice expansion (blue line with circles) of the topmost Rh surface region 3. Results and discussion between room temperature and 830 °C. As explained above, the absolute measured lattice constant of the rhodium at room tem- First we confirmed the 13-on-12 reconstruction of the (h-BN)/ perature is associated with a systematic error of ±0.01 Å, however Rh(111)-system at room temperature (see Fig. 1). Importantly, in the shape of the curve is reliable. Hence the boundaries of possible addition to the (10)-Rh-peak and the 13/12 principal (h-BN)-peak, vertical displacement of the measured lattice constant of rhodium we observe the 11/12 peak. We call this the ‘‘real reconstruction” are given by the grey band.

1 10 (a) (c) 12 14 2.73 h = 13 h = 13 0 2.72 10 h = 11 h = 13 12 12 12 2.71 11 1.09 h = 10 h = 12 [Å] 2.7

11 11 Rh

-1 a 2.69 10 2.68 13 12

2.67 h-BN (b) 1.08 -2 / a

10 2.504 14 Rh 13 a ]

o Å [

Diffraction Intensity [arb. units] 780 C 2.503 -3 o 10 25 C h-BN 2.502 1.07 0.9 1 1.1 a h [r.l.u.] 2.501 0 200 400 600 800 0 200 400 600 800 o o Fig. 1. Raw data for scans along h at l = 1.2, k = 0 r.l.u. measured at two different Temperature [ C] Temperature [ C] temperatures, 25 °C (black) and for 780 °C (magenta). The real reconstruction peak and the principal (h-BN) peak both unambiguously confirm a 13-on-12 commen- Fig. 2. (a) The temperature-dependent in-plane rhodium lattice constant, expected surate superstructure (indicated by the red dashed line) at both temperatures. The (solid blue line with grey error band) and measured (blue line with circles). (b) The 13-on-12 superstructure is unambiguous and well defined, as the peak-width is expected (h-BN) lattice expansion as given in [19]. (c) The ratio of the plots given in smaller than the separation between the h = 13/12 and the h = 14/13 positions Fig. 2a and b. At the growth temperature of 750 °C (vertical solid line) a 13-on-12 (green dotted line) or between h = 12/11 (blue dash-dotted) and h = 13/12. Note superstructure is expected, whereas at room temperature a 14-on-13 would seem that only the background increases with higher temperatures, the signals differ by more favourable. (For interpretation of the references to colour in this figure legend, less than 10% in peak height and integrated intensity. the reader is referred to the web version of this article.) SURFACE SCIENCE

LETTERS

D. Martoccia et al. / Surface Science 604 (2010) L9–L11 L11

follows: when grown, the (h-BN) forms a commensurate super- 12 -12 11 11 structure, evident from the real reconstruction peak at 11/12 ° 13 -13 r.l.u. At this temperature, 750 C, the lattice constants of rhodium 12 12 and (h-BN) favour a 13-on-12 superstructure (see Fig. 2c). During 14 -14 13 13 subsequent cooling, the strong bonding of the (h-BN) to the Rh- 0 200 400 600 800 0 200 400 600 800 substrate prohibits a change of the superstructure registry to 14- on-13, although this would be more relaxed for the (h-BN) as well 12 -12 13 13 as for the rhodium surface. The (h-BN) becomes more and more 11 -11 compressively strained, and at approximately 200 °C, this force is 12 12 strong enough to hinder the upper region of the rhodium from fur- 10 -10 11 11 ther contraction, causing this latter to become tensile strained. 0 200 400 600 800 0 200 400 600 800 o o Temperature [ C] Temperature [ C] 4. Summary and conclusions

Fig. 3. Temperature dependence of the four superstructure peaks 13/12, 13/12, In this report we have investigated the (h-BN)/Rh(111) struc- À 11/12, and 11/12 r.l.u. The reconstruction remains stable even up to above 780 °C. À ture as a function of temperature. The 13-on-12 superstructure is This proves that the reconstruction is commensurate and that 13 13 BN in fact  confirmed. The existence of a reconstruction peak at 11/12 r.l.u. lock-in to 12 12 Rh-atoms. A 14-on-13 superstructure was never observed.  proves that the system is a real commensurate superstructure caused by corrugation and not merely a flat Moiré pattern. The structure is remarkably thermally stable, with the 13-on-12 recon- ° A plot of the temperature dependent lattice expansion of bulk struction peaks remaining clearly visible up to 830 C. (h-BN) given in Eq. (2) is shown in Fig. 2b. Note that the bulk Calculations based on the thermal expansion coefficients of (h- rhodium lattice expands with temperature, whereas the (h-BN) BN) and Rh lead to the conclusion that the superstructure is formed exhibits a contraction up to 774 °C, and a dilation higher in tem- at the growth temperature. Moreover, it is proposed that the obser- perature. In Fig. 2c we show the ratio of the plots shown in vation of a hindered thermal expansion of the topmost rhodium ° Fig. 2a and b. The ratio of the measured rhodium lattice expansion surface layers below 200 C is caused by strain coupling from the and the expected (h-BN) contraction between approximately increasingly compressively strained (h-BN) layer as the system is 200 °C and the highest measured temperature of 830 °C has the cooled to the upper region of the Rh-substrate, which in turn be- same gradient as the predicted curve and therefore follows the ex- comes tensile strained. pected behaviour given by Eqs. (1) and (2). Note, however, that be- tween room temperature and 200 °C the experimental data Acknowledgements disagrees with the predicted curve insofar that the in-plane rho- dium lattice constant remains constant over this temperature This work was partly performed at the Swiss Light Source, Paul range. From Fig. 2c, one can see that at the growth temperature Scherrer Institut, Villigen, Switzerland. We thank Dominik Meister, of 750 °C the superstructure closest to both the predicted and Michael Lange and Martin Klöckner for technical support. Support experimentally determined lattice constant ratios is 13-on-12, of this work by the Schweizerischer Nationalfond zur Förderung whereas at room temperature a 14-on-13 would appear to be more der wissenschaftlichen Forschung is gratefully acknowledged. likely. The size of the measured superstructure as a function of the References temperature is shown in Fig. 3. At all temperatures up to 780 °C [1] H. Dil, J. Lobo-Checa, R. Laskowski, P. Blaha, S. Berner, J. Osterwalder, T. Greber, the peaks were found to match a 13-on-12 superstructure within Science 319 (2008) 1824. their experimental uncertainty. The errors associated with the [2] M. Corso, W. Auwärter, M. Muntwiler, A. Tamai, T. Greber, J. Osterwalder, peak positions were calculated from the standard deviation of Science 303 (2004) 217. [3] A. Goriachko, A.A. Zakharov, H. Over, J. Phys. Chem. C 112 (2008) 10423. the recorded positions and the error estimated from the pseudo- [4] S. Berner, M. Corso, R. Widmer, O. Groening, R. Laskowski, P. Blaha, K. Schwarz, Voigt fit to the signal and found to be r 0:002 r.l.u. No indica- A. Goriachko, H. Over, S. Gsell, et al., Angew. Chem. Int. Ed. 46 (2007) 5115. ¼Æ tion of a drift towards a 14-on-13 superstructure could be estab- [5] A. Goriachko, H. Over, Z. Phys. Chem. 223 (2009) 157. [6] A.B. Preobrajenski, A.S. Vinogradov, M.L. Ng, E. C´ avar, R. Westerström, A. lished, even at room temperature. This can be only explained by Mikkelsen, E. Lundgren, N. Mårtensson, Phys. Rev. B 75 (2007) 245412. the fact that the (h-BN) layer is locked in with the rhodium atoms [7] R. Laskowski, P. Blaha, T. Gallauner, K. Schwarz, Phys. Rev. Lett. 98 (2007) due to strong lock-in to the substrate, seen also by Preobrajenski 106802. et al. [20]. We know that the lock-in energy of the corrugated sys- [8] R. Laskowski, P. Blaha, J. Phys. Condens. Matter 20 (2008) 064207. [9] R. Laskowski, P. Blaha, K. Schwarz, Phys. Rev. B 78 (2008) 045409. tem is lower than the absorption energy [9], but larger than the [10] O. Bunk, M. Corso, D. Martoccia, R. Herger, P.R. Willmott, B.D. Patterson, J. strain energy. This latter is difficult to quantify for our corrugated Osterwalder, J.F. van der Veen, T. Greber, Surf. Sci. 601 (2007) L7. system, but we can set a lower limit to this for a flat (h-BN) layer, [11] F. Müller, S. Hüfner, H. Sachdev, Surf. Sci. 603 (2009) 425. [12] A. Goriachko, Y. He, M. Knapp, H. Over, Langmuir 23 (2007) 2928. which we have calculated to be 0.3 eV per superstructure cell. Cor- [13] M.T. Paffett, R.J. Simonson, P. Papin, R.T. Paine, Surf. Sci. 232 (1990) 286. rugation will of course increase this value substantially. [14] J.T. Grant, T.W. Haas, Surf. Sci. 21 (1970) 76. As the temperature was raised from 780 °C to 830 °C, the (h-BN) [15] M.C. Wu, Q. Xu, D.W. Goodman, J. Phys. Chem. 98 (1994) 5104. [16] S. Marchini, S. Günther, J. Wintterlin, Phys. Rev. B 76 (2007) 075429. superstructure and real reconstruction peaks started to irreversibly [17] D. Martoccia, P.R. Willmott, T. Brugger, M. Björck, S. Günther, C.M. Schlepütz, vanish, presumably due to thermal degradation. This caused the A. Cervellino, S.A. Pauli, B.D. Patterson, S. Marchini, J. Wintterlin, W. Moritz, diffraction peak intensities of the last temperature measurement et al., Phys. Rev. Lett. 101 (2008) 126102. [18] H.P. Singh, Acta Crystallogr. A 24 (1968) 469. to be lower, although all the peaks still matched a 13-on-12 recon- [19] R.S. Pease, Acta Crystallogr. 5 (1952) 356. struction. We propose that the anomalous lattice expansion behav- [20] A.B. Preobrajenski, M.A. Nesterov, M.L. Ng, A.S. Vinogradov, N. Mårtensson, iour of the rhodium seen in Fig. 2 up to 200 °C is explained as Chem. Phys. Lett. 446 (2007) 119.

Chapter 7 h-BN on Ru(0001) nanomesh: A 14-on-13 superstructure with 3.5 nm periodicity

The work presented in this chapter has been published in:

D. Martoccia, T. Brugger, M. Bj¨orck, C.M. Schlep¨utz, S.A. Pauli, B.D. Patterson, T. Greber, and P.R. Willmott: “h-BN on Ru(0001) nanomesh: A 14-on-13 superstructure with 3.5 nm periodicity” Surf. Sci. 604(5-6), L16-L19 (2010), doi:10.1016/J.Susc.2010.01.003 a

artikel3.pdf is the online version of the library Zentralbibliothek Z¨urich

Abstract

The structure of epitaxially grown hexagonal boron nitride (h-BN) on the surface of a Ru(0001) single crystal was investigated using surface x-ray diffraction, which clearly showed the system to form a commensurate 14-on-13 superstructure. This result disagrees with previous reports on superstructures of the same system and

–75– 76 H-BN ON RU(0001) NANOMESH: A 14-ON-13 SUPERSTRUCTURE

arguments based on simple thermal expansion coefficient calculations. We argue here that the larger observed superstructure forms because the stronger bonding of h-BN/Ru in comparison to h-BN/Rh(111) can accommodate the induced lateral in-plane strain- or lock-in energy over larger regions (referred to as the holes) within the superstructure, which itself can consequently become larger.

Reprinted with kind permission from Elsevier. a Note that you need a subscription for this journal to directly access the article. Surface Science 604 (2010) L16–L19

Contents lists available at ScienceDirect

Surface Science

journal homepage: www.elsevier.com/locate/susc

Surface Science Letters h-BN/Ru(0001) nanomesh: A 14-on-13 superstructure with 3.5 nm periodicity

D. Martoccia a, T. Brugger b, M. Björck a,1, C.M. Schlepütz a,2, S.A. Pauli a, T. Greber b, B.D. Patterson a, P.R. Willmott a,* a Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen, Switzerland b Institut of Physics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland article info abstract

Article history: The structure of epitaxially grown hexagonal boron nitride (h-BN) on the surface of a Ru(0001) single Received 4 November 2009 crystal was investigated using surface X-ray diffraction, which showed the system to form a commensu- Accepted for publication 7 January 2010 rate 14-on-13 superstructure. This result disagrees with previous reports on superstructures of the same Available online 14 January 2010 system and arguments based on simple thermal expansion coefficient calculations. We argue that the larger observed superstructure forms because of the strong bonding of h-BN to Ru. In comparison to h- Keywords: BN/Rh(111) it can accommodate more induced lateral in-plane strain- or lock-in energy over larger Boron nitride regions (referred to as the holes) within the superstructure, which itself can consequently become larger. Ru(0001) Ó 2010 Elsevier B.V. All rights reserved. Surface X-ray diffraction Superstructure Nanomesh

1. Introduction reported [15]. The periodicity of 13-on-12, as originally proposed by Paffett et al. [5], was considered to be the most likely. The formation of large superstructures on the scale of a few In a recent study, h-BN was deposited on thin Rh(111)-films nanometers, which act as nanotemplates [1] has great potential grown on yttrium stabilized zirconia on Si(111) [17]. A 14-on-13 in future applications [2]. Ideally, such templates should remain structure was reported. It was argued that the slightly smaller lat- stable and inert in air and up to high temperatures [3,4]. tice constant of the Rh-film compared to bulk Rh(111) and the

Borazine, (HBNH)3, deposited on a transition metal surface at slightly different thermal expansion coefficients are responsible high temperatures decomposes and forms a single-layer h-BN [5]. for the formation of this larger superstructure. Extrapolating this Depending on the lattice mismatch to the transition metal sub- line of argument to a Ru(0001) single crystal, it was predicted that strate, the h-BN can be either flat, or form a corrugated nanomesh either a 12-on-11 or a 13-on-12 nanomesh superstructure would structure consisting of weaker bound regions, the wires, and stron- be formed at the growth temperature of 900 K. Note that the differ- ger bound regions, the so-called holes. It has been shown that the ence in the linear dimensions of the hexagons of the h-BN between formation of h-BN on 3d- and 5d- metals, like Ni(111) [6–9] and a 13-on-12 and a 12-on-11 structure is less than 2 pm, or 0.76 % of Pt(111) [10], leads to flat layers, which are weakly bound to the the unit cell size. metal substrates. Also, on 4d-metals, the bond strength increases In order to resolve the question of the size of the h-BN/ with the unoccupied states in the d-shell of the substrate [11,12]. Ru(0001)superstructure we have performed high-resolution SXRD Bonding is weaker for growth on Pd(111) [13], and stronger on measurements. SXRD is uniquely capable of determining Rh(111) [14] and Ru(0001) [15]. This, together with the lattice lattice constants of surface structures with picometer resolution mismatch to Rh(111) and Ru(0001), results in the formation of [3,4,16,18]. a nanomesh, first observed by Corso et al. [14] on h-BN/Rh(111). The reported commensurate 13-on-12 structure was later con- 2. Experimental firmed by surface X-ray diffraction (SXRD) measurements [3,16]. In 2007, the formation of a nanomesh for h-BN on Ru(0001) was The Ru(0001) single crystal was prepared by several sputtering and annealing cycles. For the growth of the h-BN layer the crystal was heated to 1030 K in ultrahigh vacuum (UHV), and a single * Corresponding author. layer of h-BN was deposited by dosing borazine at a pressure of E-mail address: [email protected] (P.R. Willmott). 7 1 6 10À mbar for 180 s. After the growth this temperature was Present address: MAX-lab, P.O. Box 118, SE-22100 Lund, Sweden. Â 2 Present address: Physics Department, University of Michigan, Ann Arbor, MI held for another 60 s, after which, the crystal was cooled to room 48109-1120, USA. temperature over 10 min.

0039-6028/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2010.01.003 SURFACE SCIENCE

LETTERS

D. Martoccia et al. / Surface Science 604 (2010) L16–L19 L17

The resulting structure was studied in situ by low-energy elec- tron-diffraction (LEED) (Fig. 1). The LEED-image taken at an energy of 74.0 eV after the growth process shows clear satellite spots around the Ru Bragg-rod, demonstrating a well-ordered super- structure. The Ru Bragg-rod, labelled Ru in the figure, is henceforth referred to as the Ru-peak. The h-BN Bragg-rod, which we hence- forth refer to as the principal h-BN-peak, is labelled h-BN, and at 74.0 eV it is the strongest LEED signal. In addition, several other signals in a hexagonal arrangement can be identified. We call these the real reconstruction peaks for reasons that will become evident below. An example of such a real reconstruction peak is labelled rr in Fig. 1. Before we proceed, it is important to note that the weak elastic- scattering cross-section of X-ray photons with electrons means that SXRD very well satisfies the kinematical approximation of sin- gle scattering events. The low-energy electrons used in LEED, on the other hand, undergo multiple scattering and produce dynami- cal diffraction. One consequence of this is that while in SXRD real Fig. 2. He Ia (hm = 21.2 eV) normal emission photoemission spectrum of h-BN/ reconstruction peaks appear only for true commensurate super- Ru(0001). The r- and p-band splitting of about 1 eV originate from a corrugated structures, similar signals at the same positions can arise in LEED single-layer h-BN; ra and pa refer to the wires, rb and pb to the holes, which are more strongly bound. even for incommensurate overlayers. An example might be a flat structure with in-plane lattice constants marginally different from those of the substrate, which results in a flat moiré structure. A total of 18 scans were recorded, consisting of three peaks (one Hence, from the LEED pattern of Fig. 1 alone, we are unable to state real reconstruction peak, the Ru-peak and the h-BN-peak) for each with confidence whether h-BN on Ru(0001) produces such a flat of the six high-symmetry directions, namely the {h,k} = {1,0}. Each moiré structure or a true commensurate superstructure. SXRD of the 18 high-resolution scans covered ±0.04 r.l.u. in the radial can resolve this uncertainty. directions and were performed at an l-value of 0.4 r.l.u. The valence bands of h-BN/Ru(0001) recorded by ultraviolet photoelectron spectroscopy (Fig. 2) indicates splitting of the r- 3. Results and discussion and p-bands, both of which are due to a corrugation and conse- quent heterogeneous local environment (hole and wire regions) Fig. 3 shows a k-scan over the (h,k) = (0, 1)-Ru-peak. Note that in of the B and N atoms [15], the r and p peaks refer to the more a a addition to the Ru-peak, we observe the principal h-BN-peak and weakly bound wires of the corrugation, whereas the r and p b b the real reconstruction peak. Representative scans are shown in peaks are associated with the stronger bound holes. Fig. 4. It can be seen that they lie at the positions (h,k) = (0,14/13) The sample was prepared at the University of Zurich and was 9 and (h,k) = (0,12/13), respectively. The width of both peaks of transferred inside a UHV-baby chamber (10À mbar) equipped 3 6 10À r.l.u. is less than the separation between the superstruc- with a hemispherical Be-dome. After the chamber was mounted  tures under discussion (12-on-11, 13-on-12, and 14-on-13) and, on the surface diffractometer of the Materials Science beamline, from the Scherrer equation, the domain size is determined to be Swiss Light Source, the nanomesh was investigated by SXRD using of the order of 45 nm or larger. The error associated with the peak a beam energy of 12.398 keV (1.00 Å). The incident angle was 0.3°, positions was calculated from the standard deviation of the 12 peak close to the critical angle, thereby enhancing the surface sensitiv- positions and the error estimated from the pseudo-Voigt fit to the ity. The structure factors were recorded using the PILATUS 100 k 3 signal, and was found to be r = 1.4 10À r.l.u. Eleven of the 12 pixel detector and the data were extracted and corrected using  peaks lie within ±r of the nominal values. Therefore we can unam- standard procedures, described elsewhere [19–21]. biguously state that h-BN on Ru(0001) grows as 14-on-13, with a superstructure size of 3.5 nm.

-1 10

12 14 k = 13 k = 13 -2 11 13 10 k = 12 k = 12 10 12 k = 11 k = 11 -3 10 Ru h-BN -4 10 rr Diffraction Intensity [arb. units] -5 10 0.9 1 1.1 k [r.l.u.] Fig. 1. LEED pattern of h-BN/Ru(0001) taken at an energy E = 74.0 eV. The reciprocal lattice vectors h and k are indicated in red. Hexagonally arranged Fig. 3. Data of a k-scan around the (01)-peak at l = 0.4. The real reconstruction peak satellite spots (one of which is labelled rr) can be seen around the Ru-peak, labelled and the principal h-BN peak both unambiguously confirm a 14-on-13 superstruc- Ru. The principal h-BN-peak is labelled h-BN. (For interpretation of the references to ture. The appearance of a k = 12/13-peak shows that the unit cell of 13 Ru-atoms is colour in this figure legend, the reader is referred to the web version of this article.) well defined, most probably by a corrugation over this same period. LETTERS SURFACE SCIENCE L18 D. Martoccia et al. / Surface Science 604 (2010) L16–L19

This result of a 14-on-13 superstructure is in disagreement with mismatch at the growth temperature. At the growth temperature, previous LEED studies on the same system [5,15,22] and also con- the ideal match of h-BN on the Ru surface would be a 12.7-on-11.7 tradicts interpolation of data predicting a 13-on-12 or a 12-on-11 structure. The strain energy associated with stretching from a 13- superstructure on this same system [17]. Using the thermal expan- on-12 h-BN on Rh to a commensurate 1-on-1 structure has been sion coefficients for h-BN-bulk [23] and Ru-bulk [24] one would in- calculated by Laskowski et al. [27] to be 0.5 eV per BN unit. Using deed expect the superstructure with the lowest in-plane strain at the corresponding elastic constant, the energy needed for straining the growth temperature of 1030 K to be 13-on-12. On the other the h-BN lattice from an ideal match of 12.7 BN on 11.7 Ru cells to hand, at room temperature, one would expect the superstructure the observed 14-on-13 structure is calculated to be 4.3 meV per BN with the lowest in-plane strain to be 14-on-13. We have argued unit. The gain in lock-in energy for the whole superstructure cell in another study [16] detailing temperature-dependent measure- must therefore be at least 0.8 eV, since this strain energy is a lower ments on h-BN/Rh(111) that film and substrate lock in at the limit for the lock-in energy. Interestingly the calculated binding growth temperature and the strong bonding between film and sub- energy of h-BN to Ru, which was determined to be between 0.64 strate causes this superstructure to remain intact even after cool- and 0.98 eV per BN unit [27] is of the order of the minimal BN ing to room-temperature. Interestingly, in the system presented strain energy needed for the 14-on-13 superstructure. here, where bonding between the h-BN and the Ru(0001) surface is thought to be even stronger than that between h-BN and 4. Summary and conclusions Rh(111) [12], this argument fails – the observed 14-on-13 super- structure does not agree with that expected at the growth temper- In this report we have investigated the h-BN/Ru(0001) struc- ature. Even when we use the thermal expansion behaviour for Ru ture using surface X-ray diffraction. We have shown unambigu- as given in [25], where an anisotropic thermal expansion of ruthe- ously that this is a 14-on-13 superstructure. The observed size of nium is observed, the result remains the same. the superstructure contradicts previously reported studies The formation of the 14-on-13 structure may be related to the [15,17,22] and cannot be simply explained by the formation of less perfect long range order of h-BN/Ru(0001) [15] compared to the superstructure at the growth temperature, as expected from h-BN/Rh(111), though potential mechanisms for this remain ob- the lattice mismatch of bulk materials. We argue that energy min- scure. Another more interesting possibility is that the formation imization from the stronger bonding of h-BN to the Ru in compar- of the 14-on-13 superstructure might be related to the theoreti- ison to h-BN/Rh(111) overcomes the increased strain energy and cally predicted higher BN bond energy to Ru compared to that to leads to the formation of a larger superstructure, 14-on-13 rather Rh [12] and the consequently larger lock-in energy. The lock-in en- than the smaller 13-on-12. ergy depends on the BN position with respect to the substrate atoms and is largest for N on top of a substrate atom. It is expected Acknowledgements to be proportional to the bond energy to the substrate and is responsible for the formation of corrugated superstructures i.e., This work was performed at the Swiss Light Source, Paul Scher- to the formation of a dislocation network with regions of tensile rer Institut, Villigen, Switzerland. We thank Dominik Meister, Mi- strained h-BN, in the holes, where BN is strongly bound to the sub- chael Lange and Martin Klöckner for technical support and S. strate. This produces the opposite effect for the substrate atoms, Günther for providing the Ru-crystal. Support of this work by the which undergo lateral compressive strain in these strong bonding Schweizerischer Nationalfond zur Förderung der wissenschaftli- regions. The size of the holes depends on the lattice mismatch chen Forschung is gratefully acknowledged. and the bonding strength [26]. As we propose here, it is the lock- in energy that allows a stronger bonding to the substrate, hence the formation of larger holes and a 16% larger superstructure. This References offers an explanation for the formation of a larger unit cell in the case of h-BN/Ru(0001) compared to h-BN/Rh(111), whereby a lar- [1] H. Dil, J. Lobo-Checa, R. Laskowski, P. Blaha, S. Berner, J. Osterwalder, T. Greber, Science 319 (2008) 1824. ger BN lock-in energy is expected to induce the formation of a [2] A. Goriachko, H. Over, Z. Phys. Chem. 223 (2009) 157. superstructure that is larger than that expected from the lattice [3] O. Bunk, M. Corso, D. Martoccia, R. Herger, P.R. Willmott, B.D. Patterson, J. Osterwalder, J.F. van der Veen, T. Greber, Surf. Sci. 601 (2007) L7. [4] D. Martoccia, M. Björck, C.M. Schlepütz, T. Brugger, S.A. Pauli, B.D. Patterson, T. Greber, P.R. Willmott, 2009. . [5] M.T. Paffett, R.J. Simonson, P. Papin, R.T. Paine, Surf. Sci. 232 (1990) 286. a b [6] Y. Gamou, M. Terai, A. Nagashima, C. Oshima, Sci. Rep. RITU 44 (1997) 211. [7] W. Auwärter, T.J. Kreutz, T. Greber, J. Osterwalder, Surf. Sci. 429 (1999) 229. 12 14 [8] G.B. Grad, P. Blaha, K. Schwarz, W. Auwärter, T. Greber, Phys. Rev. B 68 (2003) 11 13 13 13 085404. [9] M.N. Huda, L. Kleinman, Phys. Rev. B 74 (2006) 075418. 12 Data 12 -3 -4 2 10 ´ 3 10 10 fit 12 [10] E. Cavar, R. Westerström, A. Mikkelsen, E. Lundgren, A.S. Vinogradov, M.L. Ng, 11 11 A.B. Preobrajenski, A.A. Zakharov, N. Mårtensson, Surf. Sci. 602 (2008) 1722. [11] R. Laskowski, P. Blaha, J. Phys. Condens. Matter 20 (2008) 064207. Data [12] R. Laskowski, P. Blaha, K. Schwarz, Phys. Rev. B 78 (2008) 045409. -4 2 10 fit [13] M. Morscher, M. Corso, T. Greber, J. Osterwalder, Surf. Sci. 600 (2006) 3280. [14] M. Corso, W. Auwärter, M. Muntwiler, A. Tamai, T. Greber, J. Osterwalder, -3 1 10 Science 303 (2004) 217. [15] A. Goriachko, Y. He, M. Knapp, H. Over, Langmuir 23 (2007) 2928. -4 1 10 [16] D. Martoccia, S.A. Pauli, T. Brugger, T. Greber, B.D. Patterson, P.R. Willmott, Surf. Sci., in press, doi:10.1016/j.susc.2009.12.016. [17] F. Müller, S. Hüfner, H. Sachdev, Surf. Sci. 603 (2009) 425. Diffraction Intensity [arb. units] Diffraction Intensity [arb. units] [18] D. Martoccia, P.R. Willmott, T. Brugger, M. Björck, S. Günther, C.M. Schlepütz, 0 0 A. Cervellino, S.A. Pauli, B.D. Patterson, S. Marchini, et al., Phys. Rev. Lett. 101 0.90 0.92 0.94 1.06 1.08 1.10 (2008) 126102. [19] E. Vlieg, J. Appl. Crystallogr. 30 (1997) 532. k [r.l.u.] k [r.l.u.] [20] C.M. Schlepütz, R. Herger, P.R. Willmott, B.D. Patterson, O. Bunk, C. Brönnimann, B. Henrich, G. Hülsen, E.F. Eikenberry, Acta Crystallogr. Sec. E Fig. 4. The real reconstruction peak (a) and the principal h-BN-peak (b) in units of 61 (2005) 418. the experimentally determined Ru-reciprocal lattice unit. The signals were fit using [21] C.M. Schlepütz, Ph.D. thesis, University of Zurich, 2009. a pseudo-Voigt-function. [22] A. Goriachko, A.A. Zakharov, H. Over, J. Phys. Chem. C 112 (2008) 10423. SURFACE SCIENCE

LETTERS

D. Martoccia et al. / Surface Science 604 (2010) L16–L19 L19

[23] H.P. Singh, Acta Crystallogr. A 24 (1968) 469. [26] A.B. Preobrajenski, M.A. Nesterov, M.L. Ng, A.S. Vinogradov, N. Mårtensson, [24] B. Tryon, T.M. Pollock, M.F.X. Gigliotti, K. Hemker, Scripta Mater. 50 (2004) Chem. Phys. Lett. 446 (2007) 119. 845. [27] R. Laskowski, P. Blaha, T. Gallauner, K. Schwarz, Phys. Rev. Lett. 98 (2007) [25] Thermophysical Properties of matter, vol. 12, Plenum, New York, 1975. 106802. Chapter 8

Graphene on Ru(0001): A 25×25 Supercell

The work presented in this chapter has been published in:

D. Martoccia, P.R. Willmott, T. Brugger, M. Bj¨orck, S. G¨unther, C.M. Schlep¨utz, A. Cervel- lino, S.A. Pauli, B.D. Patterson, S. Marchini, J. Wintterlin, W. Moritz, and T. Greber “Graphene on Ru(0001): A 25 × 25 supercell.” Phys. Rev. Lett. 101(12), 126102 (2008), doi:10.1103/PhysRevLett.101.126102 a

artikel4.pdf is the online version of the library Zentralbibliothek Z¨urich

Abstract

The structure of a single layer of graphene on Ru(0001) has been studied using sur- face x-ray diffraction. A surprising superstructure containing 1250 carbon atoms has been determined, whereby 25×25 graphene unit cells lie on 23×23 unit cells of Ru. Each supercell contains 2 × 2 crystallographically inequivalent subcells caused by corrugation. Strong intensity oscillations in the superstructure rods demonstrate that the Ru substrate is also significantly corrugated down to several monolayers,

–81– 82 GRAPHENE ON RU(0001): A 25×25 SUPERCELL

and that the bonding between graphene and Ru is strong and cannot be caused by van der Waals bonds. Charge transfer from the Ru substrate to the graphene expands and weakens the C–C bonds, which helps accommodate the in-plane ten- sile stress. The elucidation of this superstructure provides important information in the potential application of graphene as a template for nanocluster arrays.

Reprinted with kind permission from the American Physical Society. a Note that you need a subscription for this journal to directly access the article. week ending PRL 101, 126102 (2008) PHYSICAL REVIEW LETTERS 19 SEPTEMBER 2008

Graphene on Ru(0001): A 25 Â 25 Supercell

D. Martoccia,1 P.R. Willmott,1,* T. Brugger,2 M. Bjo¨rck,1 S. Gu¨nther,3 C. M. Schlepu¨tz,1 A. Cervellino,1 S. A. Pauli,1 B. D. Patterson,1 S. Marchini,3 J. Wintterlin,3 W. Moritz,4 and T. Greber2 1Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen, Switzerland 2Institute of Physics, University of Zu¨rich, Winterthurerstrasse 190, CH-8057 Zu¨rich, Switzerland 3Department of Chemistry, Universita¨tMu¨nchen, D-81377 Mu¨nchen, Germany 4Department of Crystallography, Universita¨tMu¨nchen, D-81377 Mu¨nchen, Germany (Received 23 July 2008; published 19 September 2008) The structure of a single layer of graphene on Ru(0001) has been studied using surface x-ray diffraction. A surprising superstructure containing 1250 carbon atoms has been determined, whereby 25 Â 25 graphene unit cells lie on 23 Â 23 unit cells of Ru. Each supercell contains 2 Â 2 crystallographically inequivalent subcells caused by corrugation. Strong intensity oscillations in the superstructure rods demonstrate that the Ru substrate is also significantly corrugated down to several monolayers and that the bonding between graphene and Ru is strong and cannot be caused by van der Waals bonds. Charge transfer from the Ru substrate to the graphene expands and weakens the C–C bonds, which helps accommodate the in-plane tensile stress. The elucidation of this superstructure provides important information in the potential application of graphene as a template for nanocluster arrays.

DOI: 10.1103/PhysRevLett.101.126102 PACS numbers: 68.65.Àk, 81.05.Uw, 81.07.Nb

The detailed structure determination of single-layer gra- has remained a contentious issue as to what registry exists phene on well-defined surfaces is a significant goal in between graphene and the underlying Ru substrate. It has materials science and solid-state physics—it is most prob- been suggested that ð12  12Þ graphene hexagons sit on able that future electronic devices based on graphene lay- ð11  11Þ Ru surface nets (described henceforth as 12-on- ers will be fabricated on crystalline substrates [1]; hence, 11) [3,5,14], while an 11-on-10 structure has also been knowledge of how substrates affect graphene is of para- proposed [6]. If one assumes an in-plane lattice constant mount importance if the latter’s structural and electronic for graphene equal to that for graphite (2.4612 A˚ ), the properties are to be tailored [2]. In addition, it has been former structure would have an in-plane tensile strain on recently discovered [3–7] that, when grown on crystalline Ru (a ¼ 2:706 A ) of 0.78%, while the latter would be transition metal surfaces, graphene can form superstruc- compressively strained by only 0.05%. tures resulting from moire´ superpositions of ðm  mÞ car- The positions of the first-order diffraction signals asso- bon hexagons on ðn  nÞ metal surface cells. It is still dis- ciated with these two superstructures are 1.100 and puted as to whether observed features within these super- 1.0909 in-plane reciprocal lattice units (r.l.u.) of the under- cells are caused by electron density fluctuations over a lying Ru lattice; i.e., they lie within less than 0.01 r.l.u. of basically flat structure [6] or whether there is an actual one another. With a conventional LEED system, one can buckling of the graphene sheet [3,8,9]. A structural clari- achieve accuracies of only about 1%–2%, excluding an fication would identify the potential of graphene in appli- unambiguous identification of the structure using this cations such as molecular recognition, single-molecule method. Only surface x-ray diffraction is capable of sensing [10], and nanocluster array templates for biologi- achieving this goal [15–17]. cal or catalytic applications [11–13]. Here we show, using Two samples of graphene were prepared on separate surface x-ray diffraction (SXRD), that graphene forms a occasions on the same sputtered and annealed Ru(0001) surprising superstructure when grown on Ru(0001), single crystal. In both cases, the crystal was heated to whereby 25  25 graphene unit cells lie commensurately 1115 K in ultrahigh vacuum (UHV), and a single layer of on 23  23 unit cells of Ru. Characteristic intensity oscil- graphene was deposited by dosing ethene at a pressure of lations in the SXRD data prove that not only the graphene 2  10À5 Pa for 3 minutes [18]. The temperature was then but also the Ru down to several atomic layers are signifi- held at 1115 K for a further 60 seconds. For the first cantly corrugated, indicating that the bonding between the sample, the crystal was then cooled at a rate of 0:4KsÀ1 single graphene layer and Ru is unusually strong. down to 915 K and from there at a rate of 0:8KsÀ1 down The structure of graphene on Ru(0001) has already been to 610 K, after which the heating was turned off. In the case investigated using scanning tunneling microscopy (STM), of the second sample, cooling was approximately 4 times conventional electron microscopy, x-ray photoelectron quicker. It is noted here that these different cooling rates spectroscopy (XPS), Raman spectroscopy, and low-energy were chosen to establish whether they affected the final electron diffraction (LEED) and microscopy [3,5–7,9,14], form of the absorbate structure. No significant difference as well as density functional theory (DFT) [8]. Until now, it between the two samples could be detected, however.

0031-9007=08=101(12)=126102(4) 126102-1 Ó 2008 The American Physical Society week ending PRL 101, 126102 (2008) PHYSICAL REVIEW LETTERS 19 SEPTEMBER 2008

Typical LEED and STM images after cooling to room signal is, at ð5:4 Æ 0:1ÞÂ10À3 r:l:u:, significantly nar- temperature are shown in Fig. 1. rower than the separation of any independent 13-on-12 The samples were transferred in UHV to a minichamber and 12-on-11 signals of 7:6 Â 10À3 r:l:u: [see Figs. 2(c) (10À7 Pa) equipped with a hemispherical Be dome for and 2(d)]. Also, a model consisting of a random distribu- studies using SXRD [19]. The chamber was mounted on tion of 13-on-12 and 12-on-11 supercells differs from that the surface diffractometer of the Materials Science beam of the 25-on-23 structure by maximum in-plane displace- line, Swiss Light Source [20]. Structure factors were re- ments of the carbon atoms of less than 0.1 A˚ , which are corded using the Pilatus 100 k pixel detector [21]. The significantly smaller than typical vibrational amplitudes at photon energy was 12.4 keV, and the transverse and lon- room temperature and hence can be ignored. gitudinal coherence lengths were both 1 m. The supercell, covering over 33 nm2 and containing A calibration of reciprocal space was achieved to two 1250 carbon atoms, is shown in the scanning tunneling parts in 10 000 by using bulk Ru Bragg reflections as microscope image in Fig. 1(b). This contains not one but reference points. A typical set of in-plane scans is shown four parallelogram structures. It is still disputed whether in Figs. 2(b)–2(d). In Fig. 2(b), satellites on either side of the hill-like features are formed by a physical corrugation the Ru (01) crystal truncation rod (CTR) can be seen. The of the graphene sheet or are caused by electron density primary graphene (01) signal [see Fig. 2(d)]atk ¼ waves in an essentially flat graphene layer [6]. Although 1:087 r:l:u: is, in itself, no proof of a commensurate recon- this cannot be decided from the STM data alone, a recent struction, as the graphene could, in principle, lie incom- combined DFT/STM study [8] revealed that the graphene mensurately above the Ru substrate. However, the presence is indeed significantly corrugated when deposited on Ru also of a signal an equal distance on the other side of the Ru (0001). It is these features that make this system so inter- CTR indicates that a reconstruction must exist [Fig. 2(c)]. esting as a potential nanotemplate. We found several other signals proving a true reconstruc- The four ‘‘subcells’’ within the supercell cannot map tion elsewhere in reciprocal space [see Fig. 2(a)]. Note that translationally onto one another, as from the SXRD data it the (0001) surface of hexagonal close-packed systems is clear that the number of unit cells of Ru (23) as well of commonly display sixfold symmetry, although the symme- graphene (25) along the edges of the supercell are odd, and try of a perfect hcp(0001) surface is threefold. This appar- one is therefore forced to conclude that the graphene super- ent increase in symmetry is caused by surfaces containing cell must consist of four translationally inequivalent sub- regions separated by atomic steps of half a unit cell height, cells. It is noted that, because of the presence of 2 Â 2 resulting in a 180 rotation of adjacent terraces. This is corrugation periods within each supercell, all superstruc- why only one in-plane axis is shown in Fig. 2(a). ture peaks with an in-plane distance from the Ru signals of The positions of the two reconstruction signals shown in p=23 r:l:u:, where p is an odd integer, are systematically Figs. 2(c) and 2(d) and those of all of the other super- absent. structure signals investigated indicate, however, that the The 21=23 and 25=23 superstructure rods (SSRs) are superstructure complies with neither of those proposed so shown in Fig. 2(e). Because they provide information only far. In fact, the signals sit exactly at 21=23 and 25=23 r.l.u., on surface reconstructions of the graphene and uppermost to within 0.0002 r.l.u. from which it is unambiguously clear Ru layers, and not on bulk properties, we are able to infer from our SXRD data that the reconstruction is in fact 25- important properties of the surface region immediately on-23, that is, 25 Â 25 graphene honeycombs sitting com- from their qualitative features. First, the signal intensity mensurately on 23 Â 23 Ru unit cells. This signal cannot is strongly modulated, with a periodicity of approximately be explained as originating from the incoherent addition of 1.0 r.l.u. (with respect to Ru) in the out-of-plane direction. diffraction signals from large domains of 13-on-12 and 12- This modulation can occur only if the ruthenium is physi- on-11 supercells, as the linewidth of the superstructure cally corrugated, that is, if the graphene imposes vertical

FIG. 1 (color online). (a) A LEED image of the graphene/Ru(0001) surface taken at an electron energy of 74 eV. (b) An STM image of graphene on Ru(0001), highlighting the supercell containing four subcells.

126102-2 week ending PRL 101, 126102 (2008) PHYSICAL REVIEW LETTERS 19 SEPTEMBER 2008

(a) (b) (c) (d)

-1 -4 h, k 10 6×10 021 3 12/11 10/11 13/12 25/23 11/12 21/23 21/23 25/23 × -5 -2 2 10 10 (e) -4 5 4×10

-3 4 21/23 10 25/23 -5 1×10 -4 3 2×10 -4 Intensity [arb. units] 10 2

1 -5 0 0 10

Diffraction Intensity [arb. units] 0.9 1 1.1 0.9 0.92 1.08 1.1 0 0 0.5 1 1.5 2 2.5 3 3.5 k [r.l.u.] k [r.l.u.] k [r.l.u.] l [r.l.u.]

FIG. 2 (color online). Summary of the diffraction data for the graphene/Ru(0001) system. (a) Schematic reciprocal space map showing where data were recorded. The red circular dots indicate points recorded in plane at l ¼ 0:4r:l:u. The in-plane scan along the k direction in the neighborhood of the (01) CTR of Ru at l ¼ 0:4r:l:u: shown in (b) is indicated by the green (gray) line. The positions of superstructure rods shown in (e) are indicated by the orange diamond and blue square. (c),(d) High-resolution scans across the superstructure signal of graphene on Ru, detailing the 25-on-23 reconstruction. The data were fit to a pseudo-Voigt profile (solid black curves), while the positions where 13-on-12 and 12-on-11 reconstruction diffraction signals would lie (dotted lines) are also shown. strain [8]. Importantly, all of the maxima have widths of depth, with a characteristic length of 1.7 unit cells approximately 0.25 r.l.u., which means that the Ru sub- (3.4 atomic layers). Note that the graphene and ruthenium strate must also be significantly corrugated down to about corrugations were chosen to be in phase (i.e., peak above 4 unit cells, or over 1.5 nm. peak and valley above valley). If the corrugations are made Unsurprisingly, the 25=23 rod has significant intensity at to be out of phase (peak above valley and valley above low l values, as at l ¼ 0 this corresponds to the (010) in- peak), the agreement with the experimental data is poorer. plane graphene peak, which is known to have nonzero The effect on the shape of the SSRs of the graphene intensity. However, extrapolation of the 21=23 rod to l ¼ corrugation amplitude is fairly insensitive, due to the low 0 strongly indicates that it also has nonzero intensity here, x-ray scattering amplitude of carbon. IðVÞ curves from which can occur only if there are in-plane movements of low-energy electron diffraction may provide important the atoms within the supercell. further quantitative information regarding the detailed gra- In order to estimate the corrugation amplitudes and phene structure, due to its higher surface sensitivity. A depths of the ruthenium, we used a simple model to simu- rigorous fit would also include in-plane movements of late the two superstructure rods of Fig. 2(e). The vertical both the carbon and Ru atoms and the possibility that the displacement field of the graphene corrugation [Fig. 3(a)] average height of each Ru atomic layer can vary. Allowing is generated by first calculating a subfield for each of the in-plane movements could significantly change the magni- two inequivalent carbon atoms in the conventional graphite tudes of the calculated corrugations; hence, their values unit cell, whereby the vertical distance to the Ru substrate given here are still tentative. is proportional to the in-plane separation from the nearest The large depth to which the ruthenium substrate is Ru atom. The component fields are interpolated and then perturbed is, however, a robust parameter and is indicative added to produce the final displacement map. The model of an attendant strong chemical bonding of graphene to the incorporated only four parameters, namely, the graphene metallic substrate via the carbon pz orbitals, which cannot corrugation amplitude and the minimum graphene-Ru dis- arise through van der Waals bonds. This has recently been tance, for which we used fixed values determined by DFT predicted by DFT calculations that find strong charge calculations [8], and the corrugation of the uppermost Ru redistributions and a minimum graphene-Ru distance of atomic layer and the exponential decay depth of the Ru only 2.2 A˚ , incompatible with van der Waals interactions corrugation, which were varied to best match the experi- [8], while XPS measurements have shown a high degree of mental linewidths and intensities. Any in-plane movements orbital hybridization between graphene and Ru(0001) [9]. of either the graphene or the Ru were ignored, as this would Strong interactions have also been seen for graphene on Ni add significant complexity to the model, and our a priori (111) [18,22]. This increased bonding to the substrate is knowledge of such movements is very limited. The simu- connected with expanded and weakened C–C bonds, as lation is shown in Fig. 3. Despite the simplicity of this indicated by the softened phonons of the graphene layer model, the qualitative agreement is impressive. The peak- [14]. to-peak corrugation amplitude of the uppermost ruthenium This in-plane expansion of the graphene layer might atomic layer is 0.20 A˚ , which decays exponentially with therefore accommodate the apparent tensile strain of the

126102-3 week ending PRL 101, 126102 (2008) PHYSICAL REVIEW LETTERS 19 SEPTEMBER 2008

(a) ideally suited as a robust template for arrays of nanoclus- ters or macromolecules. The authors thank Dr. Marie-Laure Bocquet and Mr. Bin Wang for fruitful discussions. Support of this work by the Schweizerischer Nationalfonds zur Fo¨rderung der wissen- schaftlichen Forschung and the staff of the Swiss Light Source is gratefully acknowledged. This work was partly performed at the Swiss Light Source, Paul Scherrer Institut. (b) 5

21/23 4 25/23 *[email protected] [1] A. K. Geim and K. S. Novoselov, Nature Mater. 6, 183 3 (2007). [2] K. S. Novoselov, Nature Mater. 6, 720 (2007). 2 [3] S. Marchini, S. Gu¨nther, and J. Wintterlin, Phys. Rev. B 76, 075429 (2007). 1 Diffraction Intensity [arb. units] [4] J. Coraux, A. T. N’Diaye, C. Busse, and T. Michely, Nano Lett. 8, 565 (2008). 0 [5] P. Yi, S. Dong-Xia, and G. Hong-Jun, Chin. Phys. 16, 3151 0 0.5 1 1.5 2 2.5 3 3.5 (2007). l [r.l.u.] [6] A. L. Va´zquez de Parga, F. Calleja, B. Borca, M. C. G. FIG. 3 (color online). Simple parametric model of the Passeggi, Jr., J. J. Hinarejos, F. Guinea, and R. Miranda, graphene-Ru(0001) supercell. (a) The vertical displacement field Phys. Rev. Lett. 100, 056807 (2008). of the graphene corrugation. The scale is given in angstroms [7] P. W. Sutter, J.-I. Flege, and E. A. Sutter, Nature Mater. 7, above the Ru substrate. (b) Simulated 21=23 and 25=23 super- 406 (2008). structure rods of corrugated graphene on Ru(0001), incorporat- [8] B. Wang, M.-L. Bocquet, S. Marchini, S. Gu¨nther, and J. ing the qualitative features extracted from the experimental data. Wintterlin, Phys. Chem. Chem. Phys. 10, 3530 (2008). The graphene has a peak-to-peak corrugation amplitude of 1.5 A˚ , [9] A. B. Preobrajenski, N. L. Ng, A. S. Vinogradov, and N. while that of the uppermost Ru atomic layer is 0.20 A˚ . The Ma˚rtensson, Phys. Rev. B 78, 073401 (2008). corrugation amplitude of the Ru drops exponentially by a factor [10] H. Dil, J. Lobo-Checa, R. Laskowski, P. Blaha, S. Berner, of 0.75 for each successive atomic layer (0.56 per unit cell J. Osterwalder, and T. Greber, Science 319, 1824 (2008). depth). The minimum graphene-Ru distance is 2.2 A˚ , and the [11] Y. Min, M. Akbulut, K. Kristiansen, Y. Golan, and J. mean vertical positions between all of the Ru atomic planes Israelachvili, Nature Mater. 7, 527 (2008). assume bulk values. [12] A. T. N’Diaye, S. Bleikamp, P.J. Feibelman, and T. Michely, Phys. Rev. Lett. 97, 215501 (2006). [13] H.-G. Boyen et al., Science 297, 1533 (2002). [14] M.-C. Wu, Q. Xu, and D. W. Goodman, J. Phys. Chem. 98, 25-on-23 supercell when assuming a bulklike graphite in- 5104 (1994). plane lattice constant for graphene. Indeed, allowing for an [15] A. Goriachko, Y. He, M. Knapp, H. Over, M. Corso, T. expansion of the C–C bond of approximately 1% due to Brugger, S. Berner, J. Osterwalder, and T. Greber, Langmuir 23, 2928 (2007). electron transfer would result in nominally zero heteroe- [16] R. Feidenhans’l, Surf. Sci. Rep. 10, 105 (1989). pitaxial strain for this 25-on-23 structure, although, of [17] O. Bunk, M. Corso, D. Martoccia, R. Herger, P. R. course, because we observe elastic deformation of the Ru Willmott, B. D. Patterson, J. Osterwalder, J. F. van der substrate, there must be stress in the graphene layer that Veen, and T. Greber, Surf. Sci. 601, L7 (2007). imposes strain both in itself and in the substrate. In other [18] C. Oshima and A. Nagashima, J. Phys. Condens. Matter 9, words, the Ru–C bonding causes the graphene to dilate in 1 (1997). plane and the 25-on-23 structure to have the lowest surface [19] The design of the minichamber is based on that of T.-L. energy. Lee and J. Zegenhagen of the European Synchrotron In conclusion, the structure of the supercell of graphene Research Facility, whom we gratefully acknowledge. et al. 247 on Ru(0001) has been elucidated and been shown to consist [20] P. R. Willmott , Appl. Surf. Sci. , 188 (2005). 25 25 23 23 [21] C. M. Schlepu¨tz, R. Herger, P.R. Willmott, B. D. of  unit cells of graphene on  unit cells of Patterson, O. Bunk, C. Bro¨nnimann, B. Henrich, G. Ru. On the one hand, this large in-plane extent of over 6 nm Hu¨lsen, and E. F. Eikenberry, Acta Crystallogr. Sect. A and, on the other, the large corrugation amplitudes of the 61, 418 (2005). Ru substrate, which indicate a strong bond between the [22] A. Nagashima, N. Tejima, and C. Oshima, Phys. Rev. B graphene and ruthenium, suggest that this system may be 50, 17 487 (1994).

126102-4 Chapter 9

Graphene on Ru(0001): A corrugated and chiral structure

The work presented in this chapter has been published in:

D. Martoccia, M. Bj¨orck, C.M. Schlep¨utz, T. Brugger, S.A. Pauli, B.D. Patterson, T. Greber, and P.R. Willmott: “Graphene on Ru(0001): A corrugated and chiral structure.” New J. Phys. 12, 043028 (2010), doi:10.1088/1367-2630/12/4/043028 a

artikel5.pdf is the online version of the library Zentralbibliothek Z¨urich

Abstract

We present a structural analysis of the graphene/Ru(0001) system obtained by sur- face x-ray diffraction. The data were fit using Fourier-series expanded displacement fields from an ideal bulk structure, plus the application of symmetry constraints. The shape of the observed superstructure rods proves a reconstruction of the sub- strate, induced by strong bonding of graphene to ruthenium. Both the graphene layer and the underlying substrate are corrugated, with peak-to-peak heights of

–87– 88 GRAPHENE ON RU(0001): A CORRUGATED AND CHIRAL STRUCTURE

(0.82 ± 0.15) A˚ and (0.19 ± 0.02) A˚ for the graphene and topmost Ru-atomic layer, respectively. The Ru-corrugation decays slowly over several monolayers into the bulk. The system also exhibits chirality, whereby in-plane rotation of up to 2.0o in those regions of the superstructure where the graphene is weakly bound are driven by elastic energy minimization.

Reprinted with kind permission from IOP. New Journal of Physics The open–access journal for physics

Graphene on Ru(0001): a corrugated and chiral structure

D Martoccia1, M Björck1,3, C M Schlepütz1,4, T Brugger2, S A Pauli1, B D Patterson1, T Greber2 and P R Willmott1,5 1 Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen, Switzerland 2 Institute of Physics, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland E-mail: [email protected]

New Journal of Physics 12 (2010) 043028 (12pp) Received 17 February 2010 Published 14 April 2010 Online at http://www.njp.org/ doi:10.1088/1367-2630/12/4/043028

Abstract. We present a structural analysis of the graphene/Ru(0001) system obtained by surface x-ray diffraction. The data were fitted using Fourier-series- expanded displacement fields from an ideal bulk structure plus the application of symmetry constraints. The shape of the observed superstructure rods proves a reconstruction of the substrate, induced by strong bonding of graphene to ruthenium. Both the graphene layer and the underlying substrate are corrugated, with peak-to-peak heights of (0.82 0.15) Å and (0.19 0.02) Å for graphene and the topmost Ru-atomic layer,± respectively. The Ru± corrugation decays slowly over several monolayers into the bulk. The system also exhibits chirality, whereby in-plane rotations of up to 2.0◦ in those regions of the superstructure where the graphene is weakly bound are driven by elastic energy minimization.

3 Current address: MAX-lab, PO Box 118, SE-22100 Lund, Sweden. 4 Current address: Physics Department, University of Michigan, Ann Arbor, MI 48109-1120, USA. 5 Author to whom any correspondence should be addressed.

New Journal of Physics 12 (2010) 043028 1367-2630/10/043028+12$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft 2

Contents

1. Introduction 2 2. Experimental 3 3. Results and discussion 4 4. Summary and conclusion 7 Acknowledgments 8 Appendix 8 References 11

1. Introduction

Nanostructured materials have attracted increasing interest in recent years, due to their potential in practical electronic applications. One of these, graphene, has been theoretically investigated since the 1940s [1]. The discovery in 2004 that freestanding graphene may be prepared [2] led to an explosion of interest in this material due to its unique electronic properties and possible practical utilization [3]. Graphene is a single sheet of carbon atoms arranged in a honeycomb structure, which was believed to be thermodynamically unstable under ambient conditions, due to the Mermin–Wagner theorem [4]. Nowadays the stability of graphene is explained by postulating small out-of-plane corrugations, leading to lower thermal vibrations [5, 6]. On crystalline substrates, the formation of superstructures and the concomitant corrugation of graphene provide template functionality [7]. The influence of the substrate and the formation of the superstructure are believed to change the electronic bandstructure and the electronic properties [7–10], due to bond formation and charge-transfer phenomena [7], [11–13]. The characterization of the graphene–metal interface structure is of crucial importance, because measurements of the electronic transport properties require making metallic contacts [14]. Surface x-ray diffraction (SXRD) is a powerful investigative tool for this system, since the diffraction intensity is perfectly described in a single scattering picture and is unaffected by density-of-state effects or electrostatic forces. Graphene grown on transition metals forms single-domain superstructures with high degrees of structural perfection [15–19]. Early reports on graphene on Ru(0001) proposed a superstructure in which (12 12) unit cells of graphene sit on (11 11) unit cells of ruthenium (‘12-on-11’) [15, 16], while× other studies proposed an 11-on-10 superstructure× [17]. However, recent SXRD results showed unambiguously that the reconstruction is in fact a surprisingly large 25-on-23 superstructure [18]. A comparative study between density functional theory (DFT) calculations and scanning tunneling microscopy (STM) experiments showed the structure to be composed of regions of alternating weak and strong chemical interactions of graphene with the Ru substrate [20, 21]. Here, we detail the atomic structure of the graphene/Ru(0001) system, determined with sub-angstrom resolution from SXRD data. In addition to quantifying the corrugation, we also show that the best model exhibits the formation of chiral domains, resulting in a lower symmetry (p3) compared to graphite (p3m1). This unexpected property may have an important impact on, e.g., the use of this system as a template for molecular chiral recognition, where a chiral surface allows one to distinguish between left- and right-handed absorbed enantiomers [22]. We

New Journal of Physics 12 (2010) 043028 (http://www.njp.org/) 3 argue that this symmetry breaking is driven by energy minimization based on elastic energy considerations.

2. Experimental

Sample preparation and the SXRD measurement setup at the Surface Diffraction Station of the Materials Science Beamline, Swiss Light Source, have already been detailed in [18]. It was demonstrated from simple simulations of the 25/23 superstructure rod (SSR) that the substrate must also be corrugated, since oscillations with the appropriate periodicity of approximately 1.0 out-of-plane substrate reciprocal lattice units (r.l.u., 2π/c) on the SSRs only start to appear if one includes a corrugation of the substrate. Here, we present further SXRD data from the same sample, which in addition to the SSRs now includes in-plane data. Because of the very large number of atoms involved in the superstructure, it is impossible to fit each atomic position individually. Instead, we have parametrized the structural model using a small set of physically reasonable parameters. The in-plane and out-of-plane deviations of the atomic positions from an ideal flat structure of the graphene and of the uppermost layers of the Ru substrate are described by a 2D Fourier-series expansion. We truncate this series after the fourth Fourier component, since higher orders could not be resolved in the diffraction data. The displacement field of the system is allowed to adopt the lower p3 symmetry, since this is the lowest symmetry still compatible with the apparent measured sixfold diffraction symmetry, which only arises because of the superposition of the two possible terminations of the hexagonal close-packed (hcp) substrate [23]. Because the p3 symmetry allows chiral structures, we have to sum over the signals from domains of each enantiomer and assume a 50% distribution. Details of the implementation of the Fourier expansion and of symmetry constraints are given in the appendix. Here, we discuss only those aspects that are needed to understand the results. First, it is important to note that because the 25-on-23 structure contains 2 2 corrugation periods, only the even Fourier components, that is, the second and fourth, must× be considered. This is also demonstrated by the absence of signal at the 22/23, 24/23, . . . SSRs. For each atom within the supercell, the in-plane and out-of-plane deviations ￿x, ￿y and ￿z are described by the two Fourier components. In total, both graphene and ruthenium require nine fitting parameters each in order to describe their corrugations. In addition to the 18 corrugation parameters we introduce a factor, λ, which describes an exponential decay of the substrate corrugation amplitude with substrate depth z A(z) A exp( z/λ). (1) = 0 − This decay applies to all the three amplitudes used for the description of the substrate displacement function. We fix the minimum distance from the substrate to graphene layer, dC Ru, as 2.0Å [20, 24], since our model is relatively insensitive to this parameter within physically− sensible limits ( 0.1 Å). The parameter dRu1 Ru2 is the distance between the first and second Ru- atomic layers. Lastly,± a global scaling factor− S is required, resulting in a total of 21 free-fitting parameters. We begin by defining regions of the supercell, where we consider a flat graphene layer lying commensurably 25-on-23 on top of a flat Ru substrate (see figure 1). The gray-shaded region in figure 1(b) indicates where the first of the two C atoms within a ‘normal’ graphene unit cell sits on top of an Ru atom of the topmost substrate atomic layer (red atoms), and the second atom sits on top of an Ru atom from the second substrate atomic layer (green atoms, the

New Journal of Physics 12 (2010) 043028 (http://www.njp.org/) 4 (a) (b)

Figure 1. (a) Graphene (black) on top of ruthenium (red, first layer, and green, second layer). Three regions shaded gray, green and red are highlighted and explained in the text. (b) A zoom into the lower left corner of the 25-on-23 supercell. hcp position). Henceforth, we refer to this as the (top, hcp) region. Using the same arguments, the red area is the (hcp, fcc) region and the green one is the (fcc, top) region [25]. Fitting6 was performed using GenX [26], an optimization program using the differential evolution algorithm, which helps avoid getting trapped in local minima [27]. The errors of the fitted parameters are estimated by an increase in the GOF of 5%.

We fit dRu1 Ru2 to the CTR data alone (figure 2(a)), as this is sensitive to small differences in the interplanar− spacing of the topmost two Ru-atomic layers but is largely insensitive to the form of the weakly scattering superstructure. The best fit had an R-factor of 5.2%, for dRu1 Ru2 (2.080 0.003) Å, which should be compared to a bulk value of 2.141 Å. This equates− to= a contraction± of 2.8%, in agreement with the papers [28–30].

3. Results and discussion

The starting model for the search of all the other parameters was a strained 25-on-23 flat graphene layer lying commensurably on a flat ruthenium bulk structure. The best fit for the SSR and in-plane data has an R-factor of 13.4% (figures 2(b) and (c)). The peak-to-peak corrugation height of graphene is (0.82 0.15) Å, in agreement with the papers [15, 17, 31], whereas that of the uppermost Ru-atomic± layer is (0.19 0.02) Å and is out-of-phase with respect to the graphene corrugation (figure 3). The exponential± decay length of λ (7.0 0.4) Å means that there is still approximately a tenth of the distortion of the first Ru-atomic= ± layer at a depth of four Ru-atomic layers. This strongly supports the idea of a chemisorbed graphene layer with significant interaction with the substrate [7, 24], [32–34].

6 Fitting is guided by the goodness-of-fit (GOF), here the logarithmic R-factor, used to avoid weighting the intense parts of the measured data more than the weak parts. The final fitting result is given in terms of the R-factor [39].

New Journal of Physics 12 (2010) 043028 (http://www.njp.org/) 5

(a) (b)

(c)

Figure 2. (a) The (1,0)-CTR. Only the scaling factor and dRu1 Ru2 were used to fit the data. (b) Fit of the two SSRs. (c) In-plane map of the− superstructure reflections around the (1,0)-CTR position at l 0.4r.l.u. The areas of the circles are proportional to the scattering intensities. =

Figure 3. Schematic view of the corrugation and interplanar distances of graphene and the substrate.

Details of the final structure are summarized in figure 4. Figure 4(a) shows a clear corrugation of the graphene with the hills lying in the weakly bound (hcp, fcc)-region. The hills have a triangular shape, in remarkable agreement with earlier STM data [15, 16]. Although

New Journal of Physics 12 (2010) 043028 (http://www.njp.org/) 6

Figure 4. (a) Top view of the counterclockwise twisting enantiomer resulting from the fitting procedure: the graphene shows the lowest lying atoms to be in the (top, hcp)-region, whereas the hill maxima appear in the (hcp, fcc)-regions. Clear triangular-shaped hills are observed. (b) The in-plane displacements of the same enantiomer, magnified by a factor of 10, from the ideal bulk positions. The distortions are largest on the flanks of the hills. (c) Histogram of the bond lengths in the graphene layer. The model with p3-symmetry allows the carbon hexagons to twist, and most of the bonds are stretched by less than 0.04 Å compared to the bulk bond length of graphite (1.421 Å) (blue, dashed± line) or a flat 25/23 superstructure bond length (aRu/√3 23/25 1.4373 Å) (green, dotted line). Enforcing the higher p3m1-symmetry× causes= larger distortions in the bond lengths.

New Journal of Physics 12 (2010) 043028 (http://www.njp.org/) 7 in-plane movements of up to (0.25 0.03) Å of the graphene are observed (Figure 4(b)), the bond lengths are distorted by less± than 0.1 Å. This requires a twisting motion and indeed the in-plane movements exhibit a chiral signature, in which the largest movements occur at the steepest flanks of the hills, as one might expect, based on simple elastic strain considerations. Note that this feature emerged naturally from the fitting and was not implemented a priori into the model. The biggest rotation angle of the hexagons is 2.0◦ found on the flanks as well as on top of the hills. The elastic energy was calculated to test the physical validity of the presented parametrization approach and the resulting model. It takes into account the in-plane and out- of-plane displacements of surface atoms from their ‘ideal’ positions due to the 25/23 surface reconstruction. From our model, we calculate an elastic energy [35–37] due to strain of 9.3 eV per supercell, assuming zero strain for a flat 25-on-23 graphene layer7. Fitting the data to the higher p3m1-symmetry results in an increase in elastic energy by 83%, while the R-factor of 14.7% is significantly higher than that for the p3-symmetry. Even if we were to assume zero strain for a flat graphene layer having the bulk graphite in-plane lattice constant (figure 4(c)), this has no significant influence on the energy difference between the two different symmetry models. A histogram of all the bond lengths in the graphene superstructure demonstrates that the implementation of the lower p3-symmetry allows the bond lengths to be more preserved relative to bulk graphite. Very recently, an independent study using low-energy electron-diffraction (LEED) [38] has been published on the same Ru single crystal using the same graphene preparation and characterization, where the authors claim a corrugation of the graphene layer of 1.5 Å and a corrugation of the topmost ruthenium layer of 0.23 Å. In that study, the system is described by a p3m1-symmetry and the unit cell is cut down to one of the four inequivalent sub-unit cells. Both of these measures were taken in order to reduce computational time. An SXRD simulation of the coordinates extracted from the LEED study performed led us to a similarly high R-factor of 34.0% to that of the fit results of the LEED analysis. The reason for the discrepancies, which are far outside the error bars, are not yet resolved, although possible explanations are the already-mentioned restriction to p3m1-symmetry and a 12-on-11 superstructure—a full dynamical scattering LEED calculation of the system with p3-symmetry is at present beyond computational capabilities. In addition, the fact that LEED only probes the topmost layers, while SXRD demonstrates that significant vertical displacements occur down to at least four atomic layers of the Ru substrate, might also play an important role.

4. Summary and conclusion

In summary, we have determined the graphene/Ru(0001) structure in unsurpassed detail. This was only possible by adopting a parametric Fourier description of the superstructure using only a small number of physically reasonable parameters. Up to the mirror-symmetry breaking, the final model agrees excellently with previous STM studies. We find a graphene and ruthenium corrugation peak-to-peak height of (0.82 0.15) Å and (0.19 0.02) Å, respectively. The ruthenium corrugation is out-of-phase with± that of graphene and± decays exponentially down to a depth of several ruthenium layers. Importantly, we have also discovered the new and

7 We chose the 25-on-23 lattice constant instead of that for bulk graphite because ARPES data have shown that charge transfer from the substrate to the π ∗-antibonding orbitals will dilate the in-plane bond length [40].

New Journal of Physics 12 (2010) 043028 (http://www.njp.org/) 8 potentially highly significant property of areal chirality in the in-plane movements, which are most evident on the flanks of the hills of the corrugation. We propose that this symmetry- breaking phenomenon is induced by elastic energy minimization of the graphene layer. To test the validity of this, we calculated the elastic energy of the graphene superstructure to be 9.3 eV, less than two-thirds of that for the p3m1 case.

Acknowledgments

Support for this work from the Schweizerischer Nationalfonds zur Förderurng der wissenschaftlichen Forschung and the staff of the Swiss Light Source is gratefully acknowledged. This work was performed at the Swiss Light Source, Paul Scherrer Institut.

Appendix

In the following, the implementation of the symmetry constraints and the Fourier expansion to the graphene-on-ruthenium model will be briefly described. The displacement dr of an atom sitting at point r is expressed by its two-dimensional Fourier series dr i K i sin[2π(sx + ty) + φi ], (A.1) = s,t s,t ￿s,t

i i2 i2 i i i Ks,t As,t + Bs,t ,φs,t arctan(B /A ), (A.2) = ￿ = i i i where s and t 0, 2, 4 are the orders, As,t and Bs,t are the Fourier coefficients, φs,t are the phases of the corrugation∈{ } and i x, y, z . Note that the phase of the out-of-plane displacements influences the valley and hill∈{ shapes and} positions of the corrugation allowed by the p3- symmetry (figure A.1). Since sin( f + φ) sin( f ) cos(φ) + cos( f ) sin(φ), (A.3) = by equating Ai and Bi to Ai K i cos(φi ), = (A.4) Bi K i sin(φi ), = one can rewrite equation (A.1) as dr i Ai sin[2π(sx + ty)]+Bi cos[2π(sx + ty)]. (A.5) = s,t s,t ￿s,t

The rotation operators used for the description of the p3-symmetry are R1 and R2, which in a hexagonal coordinate system describe a 120◦ rotation counterclockwise and clockwise around the origin, respectively (figure A.2); they are defined by 0 1 11 R1 − , R2 − . (A.6) = ￿1 1￿ = ￿ 10￿ − − 1 It can be easily shown that R1 R2− R. Note that dR has to fulfill the p3-symmetry constraint, which results in = ≡ 1 1 R− dr[R(r)] R dr[R− (r)] dr(r). (A.7) { }= { }= New Journal of Physics 12 (2010) 043028 (http://www.njp.org/) 9

Figure A.1. Different corrugation shapes generated by different out-of-plane phase values. The blue regions are the strongly bound ‘valleys’ and the red highlighted regions show the weakly bound ‘hills’.

Figure A.2. The p3-symmetry constraint operators. R is defined as a rotation by 1 120◦ counterclockwise around the origin, while R− is the rotation clockwise by 120◦ around the origin

i i Table A.1. The relations of the Fourier coefficients As,t and Bs,t (i x, y, z ). z z z z z z ∈{ } As,t At, (s+t)=A (s+t),s Bs,t Bt, (s+t) B (s+t),s x = −x − y y x = −x = − y y As,t At, (s+t) + At, (s+t) A (s+t),s Bs,t Bt, (s+t) + Bt, (s+t) B (s+t),s y =−x − y − =−x − y =−x − y − =− x − As,t A (s+t),s A (s+t),s At, (s+t) Bs,t B (s+t),s B (s+t),s Bt, (s+t) = − − − =− − = − − − =− −

The relations in table A.1 are obtained by inserting equations (A.5) and (A.6) into equation (A.7). Regarding the considered Fourier components in the analysis, the zeroth order is the 23/23 reflection, the first- and third-order components correspond to the 24/23 and 26/23 systematic absences, respectively, and the 25/23 to the second-order component. Hence the fourth order

New Journal of Physics 12 (2010) 043028 (http://www.njp.org/) 10

1

0

π f1 = cos[2x·(2 /23)] -1 f = 1 cos[4x·(2π/23)] Diffraction Intensity [arb. units] 2 4

f = f1 + f2 0 5 10 15 20 Number of atoms

Figure A.3. Effect of the implementation of the fourth harmonic: f1 represents the second harmonic, f2 the fourth. Their sum for an amplitude of the fourth harmonic up to 0.25 of that of the second harmonic makes the low regions flatter. refers to the 27/23 reflection, and along the h-direction (equivalent to the k-direction) one can limit (s, t) (2, 0) and (s, t) (4, 0). For the sake of simplicity, we describe here only the implementation= to the second order.= From equation (A.5) and table A.1, one can derive the following expressions for the single components of dr that describe the displacement field. We do not include the orders (s, t) for the sake of simplicity. dr z Az sin(2π 2x) + Az sin[2π( 2y)]+Az sin[2π( 2x +2y)]+Bz cos(2π 2x) = − − +Bz cos[2π( 2y)]+Bz cos[2π( 2x +2y)], (A.8) − − dr x Ax sin(2π 2x) Ay sin[2π( 2x +2y)]+(Ay Ax ) sin[2π( 2y)]+Bx cos(2π 2x) = − − − − B y cos[2π( 2x +2y)]+(B y Bx ) cos[2π( 2y)], (A.9) − − − − dr y Ay sin(2π 2x) Ax sin[2π( 2π 2y)]+(Ax Ay) sin[2π( 2x +2y)]+B y cos(2π 2x) = − − − − Bx cos[2π( 2π 2y)]+(Bx B y) cos[2π( 2x +2y)]. (A.10) − − − −

Hence, we obtain six fitting parameters for the displacement field dr, namely Ax , Ay, Az, Bx , B y and Bz. Since we lock the phase for the fourth order to be the same as that for the second order, there will be nine fitting parameters. The effect the fourth-order harmonic with a locked phase has on the structure is shown in figure A.3. For an amplitude up to 0.25 of that of the second harmonic, the low regions in the structure will be flattened out.

New Journal of Physics 12 (2010) 043028 (http://www.njp.org/) 11

References

[1] Wallace P R 1947 The band theory of graphite Phys. Rev. 71 622 [2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Electric field effect in atomically thin carbon films Science 306 666–9 [3] Geim A K and Novoselov K S 2007 The rise of graphene Nat. Mater. 6 183–91 [4] Mermin N D and Wagner H 1966 Absence of ferromagnetism or antiferromagnetism in one- or two- dimensional isotropic Heisenberg models Phys. Rev. Lett. 17 1133 [5] Meyer J C, Geim A K, Katsnelson M I, Novoselov K S, Booth T J and Roth S 2007 The structure of suspended graphene sheets Nature 446 60–3 [6] Fasolino A, Los J H and Katsnelson M I 2007 Intrinsic ripples in graphene Nat. Mater. 6 858–61 [7] Brugger T, Günther S, Wang B, Dil J H, Bocquet M-L, Osterwalder J, Wintterlin J and Greber T 2009 Comparison of electronic structure and template function of single-layer graphene and a hexagonal boron nitride nanomesh on Ru(0001) Phys. Rev. B 79 045407 [8] Wehling T O, Balatsky A V, Tsvelik A M, Katsnelson M I and Lichtenstein A I 2008 Midgap states in corrugated graphene: ab-initio calculations and effective field theory Europhys. Lett. 84 17003 [9] Park C H, Yang L, Son Y W, Cohen M L and Louie S G 2008 Anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials Nat. Phys. 4 213–7 [10] Enderlein C, Kim Y S, Bostwick A, Rotenberg E and Horn K 2010 The formation of an energy gap in graphene on ruthenium by controlling the interface New J. Phys. 12 033014 [11] Sutter P W, Flege J I and Sutter E A 2008 Epitaxial graphene on ruthenium Nat. Mater. 7 406–11 [12] Giovannetti G, Khomyakov P A, Brocks G, Karpan V M, van den Brink J and Kelly P J 2008 Doping graphene with metal contacts Phys. Rev. Lett. 101 026803 [13] Isacsson A, Jonsson L M, Kinaret J M and Jonson M 2008 Electronic superlattices in corrugated graphene Phys. Rev. B 77 035423 [14] Ishigami M, Chen J H, Cullen W G, Fuhrer M S and Williams E D 2007 Atomic structure of graphene on SiO2 Nano Lett. 7 1643–8 [15] Marchini S, Günther S and Wintterlin J 2007 Scanning tunneling microscopy of graphene on Ru(0001) Phys. Rev. B 76 075429 [16] Pan Y, Shi D-X and Gao H-J 2007 Formation of graphene on Ru(0001) surface Chin. Phys. 16 3151 [17] Vàzquez de Parga A L, Calleja F, Borca B, Passeggi M C G, Hinarejos J J, Guinea F and Miranda R 2008 Periodically rippled graphene: growth and spatially resolved electronic structure Phys. Rev. Lett. 100 056807 [18] Martoccia D et al 2008 Graphene on Ru(0001): a 25 25 supercell Phys. Rev. Lett. 101 126102 × [19] Pan Y, Zhang H, Shi D, Sun J, Du S, Liu F and Gao H 2009 Highly ordered, millimeter-scale, continuous, single-crystalline graphene monolayer formed on Ru(0001) Adv. Mater. 21 2777–80 [20] Wang B, Bocquet M L, Marchini S, Günther S and Wintterlin J 2008 Chemical origin of a graphene Moiré overlayer on Ru(0001) Phys. Chem. Chem. Phys. 10 3530–4 [21] Jiang D E, Du M H and Dai S 2009 First principles study of the graphene/Ru(0001) interface J. Chem. Phys. 130 074705 [22] Scholl D S 1998 Adsorption of chiral hydrocarbons on chiral platinum surfaces Langmuir 14 862–7 [23] de la Figuera J, Puerta J M, Cerda J I, El Gabaly F and McCarty K F 2006 Determining the structure of Ru(0001) from low-energy electron diffraction of a single terrace Surf. Sci. 600 L105–9 [24] Sutter P, Hybertsen M S, Sadowski J T and Sutter E 2009 Electronic structure of few-layer epitaxial graphene on Ru(0001) Nano Lett. 9 2654–60 [25] Grad G B, Blaha P, Schwarz K, Auwärter W and Greber T 2003 Density functional theory investigation of the geometric and spintronic structure of h-BN/Ni(111) in view of photoemission and STM experiments Phys. Rev. B 68 085404

New Journal of Physics 12 (2010) 043028 (http://www.njp.org/) 12

[26] Björck M and Andersson G 2007 GenX: an extensible x-ray reflectivity refinement program utilizing differential evolution J. Appl. Crystallogr. 40 1174–8 [27] Wormington M, Panaccione C, Matney K M and Bowen D K 1999 Characterization of structures from x-ray scattering data using genetic algorithms Phil. Trans. R. Soc. A 357 2827–48 [28] Michalk G, Moritz W, Pfnür H and Menzel D 1983 A LEED determination of the structures of Ru(001) and of CO/Ru(001)-√3 √3R30 Surf. Sci. 129 92–106 × ◦ [29] Feibelman P J, Houston J E, Davis H L and O’Neill D G 1994 Relaxation of the clean, Cu-covered and H-covered Ru(0001) surface Surf. Sci. 302 81–92 [30] Baddorf A P, Jahns V, Zehner D M, Zajonz H and Gibbs D 2002 Relaxation and thermal expansion of Ru(0001) between 300 and 1870 K and the influence of hydrogen Surf. Sci. 498 74–82 [31] Sutter E, Acharya D P, Sadowski J T and Sutter P 2009 Scanning tunneling microscopy on epitaxial bilayer graphene on ruthenium (0001) Appl. Phys. Lett. 94 133101 [32] Preobrajenski A B, Ng M L, Vinogradov A S and Mårtensson N 2008 Controlling graphene corrugation on lattice-mismatched substrates Phys. Rev. B 78 073401 [33] McCarty K F, Feibelman P J, Loginova E and Bartelt N C 2009 Kinetics and thermodynamics of carbon segregation and graphene growth on Ru(0001) Carbon 47 1806–13 [34] Sun J T, Du S X, Xiao W D, Hu H, Zhang Y Y, Li G and Gao H J 2009 Effect of strain on geometric and electronic structures of graphene on a Ru(0001) surface Chin. Phys. B 18 3008–13 [35] Keating P N 1966 Effect of invariance requirements on elastic strain energy of crystals with application to diamond structure Phys. Rev. 145 637 [36] Pedersen J S 1989 Surface relaxation by the keating model—a comparison with ab-initio calculations and x-ray-diffraction experiments Surf. Sci. 210 238–50 [37] Bunk O 1999 Bestimmung der Struktur komplexer Halbleiter-Oberflächenrekonstruktionen mit Röntgenbeu- gung PhD thesis, University of Hamburg [38] Moritz W, Wang B, Bocquet M-L, Brugger T, Greber T, Wintterlin J and Günther S 2010 Structure determination of the coincidence phase of graphene on Ru(0001) Phys. Rev. Lett. 104 136102 [39] Baddorf A P, Zehner D M, Helgesen G, Gibbs D, Sandy A R and Mochrie S G J 1993 X-ray-scattering determination of the Cu(110)-(2 3)n structure. Phys. Rev. B 48 9013–20 × [40] Wu M C, Xu Q and Goodman D W 1994 Investigations of graphitic overlayers formed from methane decomposition on Ru(0001) and Ru(1120) catalysts with scanning-tunneling-microscopy and high- resolution electron-energy-loss spectroscopy J. Phys. Chem. 98 5104–10

New Journal of Physics 12 (2010) 043028 (http://www.njp.org/) Chapter 10

Conclusions

In this thesis, structural studies using surface x-ray diffraction (SXRD) of the sp2-hybridized layers h-BN and graphene grown on rhodium and ruthenium are described. In conjunction with complementary methods, these systems have been elucidated in detail and different physical relevant parameters have been fixed with unsurpassed detail, such as the sizes of different superstructures or the corrugation height.

In Chapter 5 we have seen that h-BN growth on Rh(111) leads to a 13-on-12 superstruc- ture. The structure has been found to be stable under prolonged exposure to ambient conditions which provides an important basis for technological applications like templating and coating. Further analysis of this system in a study, where the superstructure was measured as a function of temperature (see Chapter 6), showed that the superstructure is stable in the temperature range between room temperature and 830oC. The superstructure shows no sign of a shift to- wards a different configuration, demonstrating its high thermal stability. Based on calculations on the thermal expansion coefficient, it was proposed that the compressively strained h-BN and its strong bonding to the substrate were the cause of the observed hindered thermal ex- pansion of the rhodium surface region below 250oC. Furthermore it was concluded that the superstructure is formed at the growth temperature and that while cooling down the bonding of the h-BN to the substrate is strong enough to preserve the superstructure size. At room temperature the h-BN is compressively strained, while the rhodium is tensile strained.

–101– 102 CONCLUSIONS

Similar arguments based on thermal expansion coefficients, however failed for the system h- BN/Ru(0001) (see Chapter 7). Here we had expected a lock-in to a 13-on-12 superstructure at the growth temperature, but what we observed was a 14-on-13 structure at room temperature. These findings also disagree with other reports on this same structure. We argued here that the larger superstructure forms because the stronger bonding of h-BN/Ru in comparison to h-BN/Rh(111) can accommodate the induced lateral in-plane strain- or lock-in-energy over larger regions (referred to as the holes) within the superstructure which itself consequently becomes larger. At room temperature this system would like to form a 13-on-12 structure, hence we concluded that the h-BN within this system is tensile strained, which implies the substrate is compressively strained.

When graphene is grown on Ru(0001) a corrugated commensurate superstructure is formed (see Chapter 8). We found this to assume the surprisingly large configuration of (25×25) carbon atoms on (23 × 23) ruthenium atoms. Strong intensity oscillations in the superstructure rods demonstrated that the Ru substrate is also significantly corrugated down to several monolayers, hence the bonding between graphene and Ru is strong and cannot be caused by van der Waals bonds.

This structure was further investigated in Chapter 9. Here some of the fundamental pa- rameters, e.g. the corrugation height of the graphene, were fit using GenX, a program which relies on the use of genetic algorithms. Both the graphene layer and the underlying substrate are corrugated, with peak-to-peak heights of (0.82 ± 0.15) A˚ and (0.19 ± 0.02) A˚ for the graphene and topmost Ru-atomic layer, respectively. The Ru-corrugation decays slowly over several monolayers into the bulk and is out of phase with the corrugation of the graphene. The system is also found to exhibit chirality, whereby in-plane rotation of weakly bound graphene regions by up to 2.0o is driven by elastic energy minimization. This is a result which could have significant consequences on the theoretical calculations of this system.

In conclusion it has been shown that the structure of h-BN and graphene on transition- metal surfaces can be investigated in unique detail using SXRD, despite of the fact that both these materials are weak x-ray scatterers. It is hoped that the information gained from these investigations will provide a solid basis for further experimental and theoretical studies. Curriculum Vitae

Domenico Martoccia

Date of birth October 27, 1977 Place of birth St. Gallen (SG), Switzerland Citizenship Italian

Education 1984 – 1990 Primary school: Primarschule Wildenstein, Rorscha- cherberg (SG), Switzerland 1990 – 1993 Sekundarschule Steig, Rorschacherberg (SG), Switzer- land 1993 – 1998 High school graduation: Matura Typus B, Kantons- schule Heerbrugg, Switzerland 1998 – 2004 Studies in Experimental Physics at the University of Zurich, Diploma thesis at the Institute for Biome- chanics, Swiss Federal Institute of Technology (ETH), Switzerland: Minimierung der Fehler bei der Bestim- mung der Lagerkr¨afte im Knie- und H¨uftgelenk bei All- tagsbewegungen 2005 – 2005 Scientific co-worker at the Swiss Light Source (SLS), Paul Scherrer Institut (PSI), Villigen, Switzerland 2005 – 2006 Pre-Ph.D. at the SLS, PSI, Villigen, Switzerland 2006 – 2010 Ph.D. thesis in Experimental Physics at the SLS, PSI, Villigen, and at the University of Zurich, Switzerland: Structural Studies of h-BN and Graphene Single-Layers on Transition-Metal Surfaces

–103– All publications by D. Martoccia are listed on the following pages. Publication List

Peer-reviewed articles

[1] P. R. Willmott, R. Herger, C. M. Schlep¨utz, D. Martoccia, and B. D. Patterson: “Energetic Surface Smoothing of Complex Metal-Oxide Thin Films.” Phys. Rev. Lett. 96(17), 176102 (2006), doi:10.1103/PhysRevLett.96.176102.

[2] O. Bunk, M. Corso, D. Martoccia, R. Herger, P. R. Willmott, B. D. Patter- son, J. Osterwalder, J. F. van der Veen, and T. Greber: “Surface X-ray diffrac- tion study of boron-nitride nanomesh in air.” Surf. Sci. 601(2), L7–L10 (2007), doi: 10.1016/J.Susc.2006.11.018.

[3] P. R. Willmott, S. A. Pauli, R. Herger, C. M. Schlep¨utz, D. Martoccia, B. D. Patterson, B. Delley, R. Clarke, D. Kumah, C. Cionca, and Y. Yacoby: “Structural basis for the con-

ducting interface between LaAlO3 and SrTiO3.” Phys. Rev. Lett. 99(15), 155502 (2007), doi:10.1103/PhysRevLett.99.155502.

[4] R. Herger, P. R. Willmott, C. M. Schlep¨utz, M. Bj¨orck, S. A. Pauli, D. Martoccia, B. D. Patterson, D. Kumah, R. Clarke, Y. Yacoby, and M. Dobeli: “Structure determination of

monolayer-by-monolayer grown La1−xSrxMnO3 thin films and the onset of magnetoresis- tance.” Phys. Rev. B 77(8), 085401 (2008), doi:10.1103/PhysRevB.77.085401.

[5] D. Martoccia, P. R. Willmott, T. Brugger, M. Bj¨orck, S. G¨unther, C. M. Schlep¨utz, A. Cervellino, S. A. Pauli, B. D. Patterson, S. Marchini, J. Wintterlin, W. Moritz, and T. Greber: “Graphene on Ru(0001): A 25×25 Supercell.” Phys. Rev. Lett. 101(12), 126102 (2008), doi:10.1103/PhysRevLett.101.126102.

–105– 106 NON-REVIEWED ARTICLES

[6] M. Bj¨orck, C. M. Schlep¨utz, S. A. Pauli, D. Martoccia, R. Herger, and P. R. Willmott: “Atomic imaging of thin films with surface x-ray diffraction: introducing DCAF.” J. Phys. Condens. Matter 20(44), 445006 (2008), doi:10.1088/0953-8984/20/44/445006.

[7] D. Martoccia, S. A. Pauli, T. Brugger, T. Greber, B. D. Patterson, and P. R. Willmott: “h−BN on Rh(111): Persistence of a commensurate 13-on-12 superstructure up to high temperatures.” Surf. Sci. 604(5-6), L9–L11 (2010), doi:10.1016/J.Susc.2009.12.016.

[8] D. Martoccia, M. Bj¨orck, C. M. Schlep¨utz, S. A. Pauli, T. Brugger, T. Greber, B. D. Pat- terson, and P. R. Willmott: “h-BN/Ru(0001) nanomesh: A 14-on-13 superstructure with 3.5 nm periodicity.” Surf. Sci. 604(5-6), L16–L19 (2010), doi:10.1016/J.Susc.2010.01.003.

[9] D. Martoccia, M. Bj¨orck, C. M. Schlep¨utz, T. Brugger, S. A. Pauli, B. D. Patterson, T. Greber, and P. R. Willmott: “Graphene on Ru(0001): A corrugated and chiral struc- ture.” New J. Phys. 12, 043028 (2010), doi:10.1088/1367-2630/12/4/043028.

[10] C. M. Schlep¨utz, M. Bj¨orck, E. Koller, S. A. Pauli, D. Martoccia, O. Fischer, and P. R.

Willmott: “Structure of ultrathin heteroepitaxial superconducting YBa2Cu3O7−x films.” Phys. Rev. B 81(17), 174520 (2010), doi:10.1103/Physrevb.81.174520.

Non-reviewed articles

[1] P. R. Willmott, R. R. Herger, C. M. Schlep¨utz, D. Martoccia, and B. D. Patterson: “Techni- cal Reports: Pulsed Laser Deposition and in situ Surface X-ray Diffraction at the Materials Science Beamline at the Swiss Light Source.” Synchrotron Rad. News 18,(4), 37–42 (2005), doi:10.1080/08940880500457230.

[2] C. M. Schlep¨utz, P. R. Willmott, S. A. Pauli, R. Herger, D. Martoccia, M. Bj¨orck, D. Kumah, R. Clarke, and Y. Yacoby: “Surface x-ray diffraction of complex metal ox- ide surfaces and interfaces - a new era.” AIP Conf. Proc. 1092, 9–12 (2009).